Phy Notes Manhatten

Chapter 1 Light and Reflection by Mirrors 1.1 Light 1.2 Reflection of Light 1.3 Curved Mirrors

Section 1.1

Light • Properties of light • Luminous and non-luminous objects • Light rays and light beams

1.1 Light (SB p.3)

Properties of light

Why is there an image? Reason: Light travels in straight lines When light is blocked by an object forms an object-liked shadow

1.1 Light (SB p.4)

Properties of light

Why can light heat up an object and power a solar calculator?

Reason: Light is a form of energy

Luminous and non-luminous objects

1.1 Light (SB p.4)

Why can we see objects around us? Reason: Light from these objects enters our eyes

Objects

luminous non-luminous

emit light by themselves cannot emit light

Luminous and non-luminous objects

1.1 Light (SB p.4)

Objects

luminous

emit light by themselves

non-luminous

cannot emit light

Which of the following is/are luminous object(s)?

 



Luminous and non-luminous objects

1.1 Light (SB p.5)

Objects

luminous

emit light by themselves

non-luminous cannot emit light Why can we see non-luminous objects? Which of the following is non-luminous object?



Reason: They reflect light from other luminous sources



1.1 Light (SB p.5)

Light rays and light beams

Light ray — path for the propagation of light One light ray

Three light rays

1.1 Light (SB p.5)

divergent

Light rays parallel

Light rays and light beams

convergent

1.1 Light (SB p.5)

divergent

Light rays parallel

Light rays and light beams

convergent

1.1 Light (SB p.5)

divergent

Light rays parallel

Light rays and light beams

convergent

1.1 Light (SB p.6)

Light rays and light beams

Light beam — collection of light rays

1.1 Light (SB p.6)

Light rays and light beams

Look at an object — light rays from the object enter our eyes Diagrammatic representation — only draw two light — illustrate the size: draw two light rays rays to the eye from the tip and the foot of the object to the eye

1.1 Light (SB p.6)

Light rays and light beams

From a near object — diverging rays From a very far object — parallel rays from near object

from very far object

Section 1.2

Reflection of Light • Laws of reflection • Formation of image by plane mirror • Applications of plane mirrors

1.2 Reflection of light (SB p.6)

Reflection — when a light ray strikes a surface, it is reflected from the surface incident ray

reflected ray

1.2 Reflection of light (SB p.6)

Incident ray — incoming light ray on the mirror Reflected ray — light ray reflected from the mirror

incident ray

reflected ray

1.2 Reflection of light (SB p.6)

Normal — an imaginary line perpendicular to the surface at which the light ray strikes incident ray

normal

reflected ray

Incident point

1.2 Reflection of light (SB p.7)

Angle of incidence (i) —

angle between the incident ray and the normal

Angle of reflection (r) —

angle between the reflected ray and the normal

incident ray

normal

i

reflected ray

r

1.2 Reflection of light (SB p.7)

Laws of reflection

Experiment 1A: Reflection of light by a plane mirror Intro. VCD

Expt. VCD

Laws of reflection

1.2 Reflection of light (SB p.8)

Laws of reflection: (i) Angle of reflection (r) = Angle of incidence (i) (ii) The incident ray , the reflected ray and the normal all lie in the same plane incident ray

normal

reflected ray

1.2 Reflection of light (SB p.8)

Laws of reflection

When parallel light rays are incident on a smooth surface — regular reflection — reflected rays are parallel rough surface — sharp and clear image

1.2 Reflection of light (SB p.9)

Laws of reflection

When parallel light rays are incident on a smooth surface — regular reflection diffuse reflection rough surface — — reflected rays are not parallel — blurred image

1.2 Reflection of light (SB p.10)

Formation of image by plane mirror

Plane mirror — plane glass, coated with a thin layer of metal — regular reflection takes place (form clear images) glass

thin layer of metal coating

1.2 Reflection of light (SB p.10)

Formation of image by plane mirror

Experiment 1B: Formation of image by a plane mirror Expt. VCD

1.2 Reflection of light (SB p.11)

Formation of image by plane mirror

When the reflected rays are extended backwards, they meet at a point (position of the image (I)) light bulb image of the light bulb

1.2 Reflection of light (SB p.11)

Formation of image by plane mirror

Distance between the object and the mirror = Distance between the image and the mirror Object distance (u) = Image distance (v) light bulb

1.2 Reflection of light (SB p.12)

Formation of image by plane mirror

Construction rules for images formed by plane mirror 1. Draw an arrow (object) 2. Draw the reflected rays from the tip of the arrow (laws of reflection) object

image

3. Extend the reflected rays backwards 4. Draw the reflected rays from the foot of the arrow 5. Draw a dotted arrow (image)

1.2 Reflection of light (SB p.12)

Formation of image by plane mirror

Nature of image formed by plane mirror object

image

1. virtual image 2. same size as the object 3. erect 4. laterally inverted 5. object distance (u) = image distance (v) v

u

No light rays are come from the image, so it cannot be formed on the screen

1.2 Reflection of light (SB p.13)

Formation of image by plane mirror

Class Practice 1 ： An object (O), represented by an arrow, is placed in front of a plane mirror. Four rays, p, q, r and s are drawn from the object to the mirror as shown in the following figure. Draw the reflected rays and locate the image (I). p q object

image

r s

Ans wer

1.2 Reflection of light (SB p.14)

Formation of image by plane mirror

Class Practice 2 : A clock is placed in front of a plane mirror. What is the time shown in the clock?

10:10

Ans wer

1.2 Reflection of light (SB p.15)

Applications of plane mirrors

Applications of plane mirrors 1. Rear-view mirror — see the traffic behind — images are laterally inverted

The words are laterally inverted

1.2 Reflection of light (SB p.16)

Applications of plane mirrors

2. Periscope — see things over an obstacle ray from far object

1.2 Reflection of light (SB p.17)

3. Dressing mirror — used in washrooms and fitting rooms

Applications of plane mirrors

4. Interior decoration — make a place look spacious

Section 1.3 Curved Mirrors • Terminology for curved mirrors • Construction rules for images formed by curved mirrors • Formation of images by curved mirrors • Magnification • Image nature of curved mirrors • Finding the focal length of a concave mirror • Applications of concave mirrors • Applications of convex mirrors

1.3 Curved mirrors (SB p.19)

Curved mirrors

concave mirrors — convex mirrors —

reflecting surface convex mirror

reflecting surface curves inwards reflecting surface curves outwards

reflecting surface concave mirror

1.3 Curved mirrors (SB p.19)

Curved mirrors

cylindrical mirrors spherical mirrors

cylindrical concave mirror

inner reflecting cylindrical surface of a concave mirror — cylinder

outer reflecting cylindrical surface of a convex mirror — cylinder

cylindrical concave mirror

cylindrical convex mirror cylindrical convex mirror

1.3 Curved mirrors (SB p.19)

Curved mirrors

cylindrical mirrors spherical mirrors

spherical concave mirror — inner reflecting surface of a sphere

spherical convex mirror — outer reflecting surface of a sphere

spherical concave mirror

spherical convex mirror

spherical convex mirror

spherical concave mirror

1.3 Curved mirrors (SB p.20)

When parallel light rays are incident on a concave mirror — reflected rays converge —converging mirror

convex mirror — reflected rays diverge — diverging mirror concave mirror

convex mirror

1.3 Curved mirrors (SB p.20)

Terminology for curved mirrors

Terminology for curved mirrors concave mirror

1. pole (P) 2. centre of curvature (C) 3. radius of curvature (r) 4. principal axis convex mirror

radius 4.1.3. principal pole (P)of axis 2. centre of curvature (r) curvature (C)

1.3 Curved mirrors (SB p.21)

Terminology for curved mirrors

Experiment 1C: Reflection of light by concave and convex mirrors Expt. VCD

1.3 Curved mirrors (SB p.22)

Terminology for curved mirrors

When parallel light rays are incident on a concave mirror — reflected light rays converge convex mirror — to a point — principal focus or focus (F) focus (F)

principal axis

1.3 Curved mirrors (SB p.22)

Terminology for curved mirrors

When parallel light rays are incident on a concave mirror — reflected rays converge to a point convex mirror — reflected rays diverge, when they extended backwards, they meet at a point — focus (F) focus (F)

Terminology for curved mirrors

1.3 Curved mirrors (SB p.22)

Focal plane — cuts F, perpendicular to the principal axis

Focal length ( f ) —

distance between F and P 1 =— r 2

focal plane

focal plane

1.3 Curved mirrors (SB p.22)

Graphical symbols concave mirror

Construction rules for images formed by curved mirrors

convex mirror

1.3 Curved mirrors (SB p.23)

Construction rules for images formed by curved mirrors

Construction rules for images formed by concave mirrors 1. Parallel to the principal axis

　

pass through F

1.3 Curved mirrors (SB p.23)

Construction rules for images formed by curved mirrors

Construction rules for images formed by concave mirrors 2. Towards F 　

parallel to the principal axis

1.3 Curved mirrors (SB p.23)

Construction rules for images formed by curved mirrors

Construction rules for images formed by concave mirrors 3. Towards C 　

reflected along the same path as the incident ray

1.3 Curved mirrors (SB p.23)

Construction rules for images formed by curved mirrors

Construction rules for images formed by concave mirrors 4. Strikes the pole at an angle 　

r=i

i r

1.3 Curved mirrors (SB p.23)

Construction rules for images formed by curved mirrors

Principal of reversibility of light

Ray 2 is the reverse of ray 1 ray 1

Reason: Principal of reversibility of light If a light ray is reversed in direction 　

ray 2

light ray will retrace its original path

1.3 Curved mirrors (SB p.24)

Construction rules for images formed by curved mirrors

Construction rules for images formed by convex mirrors 1. Parallel to the principal axis 　

passes through F after extended backwards

1.3 Curved mirrors (SB p.24)

Construction rules for images formed by curved mirrors

Construction rules for images formed by convex mirrors 2. Towards F 　

parallel to the principal axis

1.3 Curved mirrors (SB p.24)

Construction rules for images formed by curved mirrors

Construction rules for images formed by convex mirrors 3. Towards C 　

reflected along the same path as the incident ray

1.3 Curved mirrors (SB p.24)

Construction rules for images formed by curved mirrors

Construction rules for images formed by convex mirrors 4. Strikes the pole at an angle 　

r=i

i r

1.3 Curved mirrors (SB p.25)

Formation of images by curved mirrors

Experiment 1D: Formation of image by concave and convex mirrors

Expt. VCD

1.3 Curved mirrors (SB p.26)

Formation of images by curved mirrors

Locate the images formed by concave mirror using graphical method 1. Draw an arrow (object) 2. Draw two special light rays from the tip of the object 3. Draw the reflected rays to meet at a point 4. Draw an arrow (image)

Nature of images formed by a concave mirror — changes with the position of the object

1.3 Curved mirrors (SB p.26)

Formation of images by curved mirrors

Locate the images formed by convex mirror using graphical method 1. Draw an arrow (object) 2. Draw two special light rays from the tip of the object 3. Extend the reflected rays backwards and intersect at a point 4. Draw a dotted line arrow (image)

Nature of images formed by a convex mirror — inverted, virtual and diminished Note: Virtual images cannot be formed on the screen, you observe them by looking into the mirrors directly.

Magnification

1.3 Curved mirrors (SB p.27)

Magnification (m) = =

Height of image (hi) Height of object (ho) Image distance (v) Object distance (u) concave mirror

u ho similar triangles

principal axis

hi v

m (plane mirror) = 1

1.3 Curved mirrors (SB p.28)

Magnification

Class Practice 3 (a)

An object (O) is placed at 20 cm in front of a concave mirror of focal length 40 cm as shown in the following figure. Draw two light rays to locate the image (I). Use a scale of 1 cm to represent 10 cm in the horizontal axis.

I

Ans wer

Magnification

1.3 Curved mirrors (SB p.29)

Class Practice 3 (Cont’d) (b) Find the image distance. Hence, find the magnification. Image distance = ______________

4 × 10 = 40 cm Magnification = = =

( 　 Image distance 　　 ) ( 　　 　 　　 ) Object distance 40 ( 　　　　　 ) ( 　　　　 　 ) 20 Ans 2

wer

1.3 Curved mirrors (SB p.30)

Magnification

Class Practice 4 (a)

The positions of an object and its image formed by a convex mirror are shown in the following figure. Locate the principal focus (F) of the mirror in the figure.

Ans wer

Magnification

1.3 Curved mirrors (SB p.30)

Class Practice 4 (Cont’d) (b) Find the focal length and magnification of the mirror. Use a scale of 1 cm to represent 2 cm in the horizontal axis. Focal length of the mirror =

4 × 2 = 8 cm

Magnification =

= =

( 　Image distance 　　 ) Object distance ( 　　 　 　　 ) 2× 2 ( 　　　　　 ) 4× 2 ( 　　　　 　 ) 0.5

Ans wer

Image nature of curved mirrors

1.3 Curved mirrors (SB p.31)

Nature of image formed by a concave mirror 1. Object is placed between P and F

image

object

• Image is formed behind the mirror • Nature of image —virtual —erect —laterally inverted —magnified (m > 1)

Image nature of curved mirrors

1.3 Curved mirrors (SB p.31)

Nature of image formed by a concave mirror 2. Object is placed at F

• Image is formed at infinity object

• Nature of image — cannot be determined

1.3 Curved mirrors (SB p.31)

Image nature of curved mirrors

Nature of image formed by a concave mirror

object

3. Object is placed between F and C • Image is formed beyond C • Nature of image — real image — inverted — magnified (m > 1)

Image nature of curved mirrors

1.3 Curved mirrors (SB p.32)

Nature of image formed by a concave mirror 4. Object is placed at C

• Image is formed

object

image

at C • Nature of image — real — inverted — same size as the object (m = 1)

Image nature of curved mirrors

1.3 Curved mirrors (SB p.32)

Nature of image formed by a concave mirror 5. Object is placed beyond C

• Image is formed

object

image

between C and F • Nature of image — real — inverted — diminished (m < 1)

1.3 Curved mirrors (SB p.32)

Image nature of curved mirrors

Nature of image formed by a concave mirror

image

6. Object is placed at infinity • Image is formed on the focal plane • Nature of image — real — inverted — diminished (m < 1)

Image nature of curved mirrors

1.3 Curved mirrors (SB p.32)

Class Practice 5 : The figure shows the image formed when a toy is placed in front of a concave mirror.

(a) State the nature of the image. The image is virtual, erect and magnified. (b) State the approximate position of the toy being placed. The toy is placed

.

between F and the mirror Ans wer

1.3 Curved mirrors (SB p.33)

Image nature of curved mirrors

Nature of image formed by a convex mirror Object is placed at any position • Image is formed between F and P • Nature of image image — virtual — erect — diminished object (m < 1) Note: When the object is — laterally placed at infinity, the image is inverted formed on the focal plane.

1.3 Curved mirrors (SB p.34)

Image nature of curved mirrors

Class Practice 6 : A toy is placed in front of a convex mirror at two different object distances. The images formed are as follows:

case 1

case 2

Image nature of curved mirrors

1.3 Curved mirrors (SB p.34)

Class Practice 6 (Cont’d) Use a ray diagram to account for the difference in image size.

The image size in case 1 is

than thatlarger in case 2 because .

the toy is placed nearer to the mirror

Ans wer

1.3 Curved mirrors (SB p.35)

Finding the focal length of a concave mirror

Experiment 1E: Finding the focal length of a concave mirror Expt. VCD

1.3 Curved mirrors (SB p.35)

Finding the focal length of a concave mirror

Object at infinity concave mirror converges the parallel rays on the focal plane Image distance = Focal length of the concave mirror parallel light rays

principal axis

focal plane

focal length (f)

1.3 Curved mirrors (SB p.36)

Finding the focal length of a concave mirror

Alternative method to find the focal length of a concave mirror Object at C of a concave mirror — Size of image = Size of object — Image distance = Object distance = r

r f= 2

r

object

image

Applications of concave mirrors

1.3 Curved mirrors (SB p.37)

Applications of concave mirrors 1. Shaving and makeup mirrors

2. Solar furnace

Faces within F of the mirror — magnified and erect image

Sunlight converges to the focus — high light intensity and temperature at the focus

1.3 Curved mirrors (SB p.38)

Applications of concave mirrors

3. Reflector Light source at the focus of the concave mirror — reflected beams are parallel Torches

D

u o y o

? Concave mirror e p a h s used in in al surgery

c i r e Car headlamp t sph o n e r a s r o t c e l f e r w o n k

1.3 Curved mirrors (SB p.39)

Applications of concave mirrors

3. Reflectors Spherical concave mirror Not all reflected rays can converge to the focus



Parabolic concave mirror All reflected rays can converge to the focus



1.3 Curved mirrors (SB p.39)

Applications of concave mirrors

4. Reflecting telescope

plane mirror

eyepiece

1.3 Curved mirrors (SB p.40)

Applications of convex mirrors

Applications of convex mirrors plane mirror

convex mirror

provides a wider field of view  image formed is diminished

1.3 Curved mirrors (SB p.40)

Applications of convex mirrors

1. Rear-view mirror — see the things behind

2. Security mirror — prevent shoplifting

3. Road safety mirror — see round a bend

Chapter 2 Refraction 2.1 Refraction of Light 2.2 Laws of Refraction 2.3 Examples of Refraction 2.4 Total Internal Reflection Manhattan Press (H.K.) Ltd. © 2001

Section 2.1 Refraction of Light

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2.1 Refraction of light (SB p.53)

Refraction — when light ray travels from one medium to another medium travelling direction of the light ray changes air refracted ray incident ray glass

84

emerging ray

Note:Light ray can travel in different media (e.g. air, water and glass).

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2.1 Refraction of light (SB p.53)

Where does the light ray refract in the glass? Refraction 2 ： from glass to air glass air

85

air

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Refraction 1: from air to glass

2.1 Refraction of light (SB p.53)

Light ray is directed towards the glass block normally — without deviation

emerging incident ray refracted ray ray

86

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Section 2.2 Laws of Refraction • Refractive index

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2.2 Laws of refraction (SB p.54)

When a light ray travels from air to glass, light ray

reflected ray (weak) refracted ray (strong)

incident ray

reflected ray

air glass

refracted ray 88

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interface

2.2 Laws of refraction (SB p.54)

Normal — pass through incident point, perpendicular to the air-glass interface incident ray

Incident point

normal

reflected ray

air glass

refracted ray 89

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interface

2.2 Laws of refraction (SB p.54)

Angle of incidence (i) —

angle between the incident ray and the normal

Angle of refraction (r) —

angle between the refracted ray and the normal

incident ray

norma l

reflected ray

i air

r

glass

refracted ray 90

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interface

2.2 Laws of refraction (SB p.54)

Experiment 2A: Refractive index of glass Intro. VCD

Expt. VCD

91

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2.2 Laws of refraction (SB p.55)

A light ray travels from air to glass obliquely It bends towards the normal

normal

original path of the light ray

92

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2.2 Laws of refraction (SB p.55)

Graph of sin i against sin r 1. pass through the origin 2.

sin i = constant sin r

93

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2.2 Laws of refraction (SB p.56)

Laws of refraction 1. The incident ray, the refracted ray and the normal all lie in the same plane

2.

incident ray

normal

sin i = constant sin r

Note: It is also called Snell’s law. 94

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weak reflected ray Interface air glass strong refracted ray

Refractive index

2.2 Laws of refraction (SB p.56)

When a light ray travels from

1. air to glass — refracted ray bends towards the normal 2. glass to air — refracted ray bends away from the normal (principle of reversibility of light) normal

95

normal air

air

glass

glass

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Refractive index

2.2 Laws of refraction (SB p.56)

Refractive index When a light ray travels from air to glass Refractive index of glass (ng) sin i = sin r sin θ ng = sin θ 96

normal

i

air

r

a g

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glass

Refractive index

2.2 Laws of refraction (SB p.57)

What is the refractive index of glass (ng)? Method 1 ng = Slope of the graph = 1.5

Method 2 Apply the equation: ng

97

=

sin θ

a

sin θ

g

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Refractive index

2.2 Laws of refraction (SB p.57)

Refractive indices of some materials Material 物質 Vacuum 真空 Air 空氣

水 Water Alcohol 酒精 Perspex 透明膠 Glass 玻璃 Diamond 鑽石

98

(n) (n) Refractive 折射率index 1.00 1.0003 ≈ 1.00 1.33 1.36 1.50 1.50 – 1.70 2.42

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Refractive index

2.2 Laws of refraction (SB p.57)

Different materials have different refractive indices

different angle of refraction (r1 ≠ r2)

normal

normal

nw = 1.33

ng = 1.5 air

air

r1

99

water

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r2

glass

Refractive index

2.2 Laws of refraction (SB p.58)

nw (1.33) < ng (1.5) refracted ray in glass bends towards the normal more (r1 > r2) normal

normal

nw = 1.33

ng = 1.5 air

air

r1

100

water

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r2

glass

2.2 Laws of refraction (SB p.58)

Refractive index

Optically denser medium — a medium with greater n a medium with Optically less dense medium — smaller n glass (ng = 1.5) — optically denser medium water (n = 1.33) — optically less dense medium w

normal

normal

nw = 1.33 air water

101

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ng = 1.5 air glass

Refractive index

2.2 Laws of refraction (SB p.58)

A light ray travels from an optically less dense medium → optically denser medium normal

refracted ray bends towards the normal optically less dense medium optically denser medium

102

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Refractive index

2.2 Laws of refraction (SB p.58)

A light ray travels from an optically denser medium → optically less dense medium normal

optically denser medium optically less dense medium

103

refracted ray bends away from the normal

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Refractive index

2.2 Laws of refraction (SB p.59)

Class Practice 1: A light ray travels from air to water as shown in the following figure. (a)

Find the angle of reflection and the angle of refraction. The refractive index of water (nw) is 1.33. Angle of reflection

=_______

air water

75o By由斯 Snell’s Law, η w = 耳定律，

sin θ a sin θ w

sin 75° 1.33 = sin θ w

θ w = 46.6° 104

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Answer ！ Click for answer now!!

Refractive index

2.2 Laws of refraction (SB p.60)

Class Practice 1 (Cont’d) (b) Sketch the reflected and refracted rays in the figure. reflected ray air air water water refracted ray

Answer ！ Click for answer now!! 105

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Refractive index

2.2 Laws of refraction (SB p.60)

Class Practice 2 : A light ray travels through a glass prism as shown in the following figure. The refractive index of the prism is 1.5. Find the angles i, a, b, c and d. Hence, find angle r. i = 90° − 45° = 45° sin i = 1. 5 sin a a = 28.1° b = 90° − 28.1° = 61.9° c = 180° − 60° − 61.9° = 58.1° d = 90° − 58.1° = 31.9° sin r = 1. 5 sin d ∴ r = 52.4° 106

normal

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Answer ！ Click for answer now!!

Section 2.3 Examples of Refraction • Real depth and apparent depth • Refraction by prism

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2.3 Examples of refraction (SB p.61)

Experiment 2B: Refraction of light Expt. VCD

108

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2.3 Examples of refraction (SB p.62)

Light rays cannot reach the eye

Real depth and apparent depth

Light rays are refracted at the water-air interface — light rays can reach the eye

in the absence of water

Refracted rays extend backwards (dotted lines) and meet at a point (position of image) air water

Note: The object appears raised. 109

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2.3 Examples of refraction (SB p.62)

Real depth and apparent depth

distance between the water Real depth (D ) — surface and the object Apparent depth (D’) — distance between the water surface and the image apparent depth

real depth

110

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Refraction by prism

2.3 Examples of refraction (SB p.63)

Prism — triangular glass prism

— when a white light passes through it, a spectrum of different colours is formed

red orange yellow green blue indigo violet

white light

prism

111

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spectrum

Refraction by prism

2.3 Examples of refraction (SB p.63)

Why is a spectrum formed? Reason: White light consists of different colours different colours have different refractive indices refract at different angles of refraction

red orange yellow green blue indigo violet

white light prism

dispersion of white light 112

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Refraction by prism

2.3 Examples of refraction (SB p.64)

Class Practice 3: A huntsman sees a shark in the water as shown in the figure below. apparent position of the shark

shark

(a) Locate the apparent position of the shark in the figure. Answer! Click for answer now!! 113

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2.3 Examples of refraction (SB p.64)

Refraction by prism

Class Practice 3 (Cont’d) larger (b) The shark appears to be (smaller/larger) in size, because the shark appears to be at a position nearer to (farther away from/nearer to ) the water surface.

Answer! Click for answer now!! 114

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Section 2.4 Total Internal Reflection • • •

Critical angle Examples of total internal reflection Applications of total internal reflection Manhattan Press (H.K.) Ltd. © 2001

2.4 Total internal reflection (SB p.65)

When a light ray travels from an optically denser medium (water) to an optically less dense medium (air) refracted ray bends away from the normal normal air

partial refracted ray

water

incident ray 116

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2.4 Total internal reflection (SB p.65)

At a small angle of incidence (i)

refracted ray (strong) reflected ray (weak)

normal air

partial refracted ray

water

incident ray

117

partial reflected ray

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2.4 Total internal reflection (SB p.65)

At a larger angle of incidence (i)

refracted ray (weaker) reflected ray (stronger)

normal air

partial refracted ray

water

incident ray

118

partial reflected ray

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2.4 Total internal reflection (SB p.65)

Angle of refraction r = 90°

refracted ray (weak)

reflected ray (strong) angle of incidence (i) = critical angle (c) normal partial refracted ray

air water incident ray critical angle (c) 119

i partial reflected ray

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2.4 Total internal reflection (SB p.65)

Angle of incidence (i) > Critical angle

no refracted ray

reflected ray only This phenomenon is called total internal reflection normal air water incident ray

120

i

i total reflected ray

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2.4 Total internal reflection (SB p.66)

Two conditions for the occurrence of total internal reflection 1. Light ray travels from an optically denser medium (water) to an optically less dense medium (air)

normal air water incident ray

total reflected ray

2. Angle of incidence (i) > Critical angle (c) of the optically denser medium (water) 121

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2.4 Total internal reflection (SB p.66)

Experiment 2C: Critical angle and total internal reflection Expt. VCD

122

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Critical angle

2.4 Total internal reflection (SB p.68)

Calculate the critical angle (c) of glass By Snell’s Law, air glass

ng =sin θ sin θ

g

sin 90o = sin c 1 –1 c = sin ( ) ng

ng = 1.5 123

a

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c = 42o

Critical angle

2.4 Total internal reflection (SB p.68)

Critical angles of some materials c = sin–1 ( 1 ) n Material 物質

(n)(n) Refractive 折射率index

Critical angle (c) (c) 臨界角

Water 水

1.33 1.50 2.42

1 ( ) = 48 .8° 1.33 1 sin −1 ( ) = 41 .8° 1.5 1 sin −1 ( ) = 24 .4° 2.42

Glass 玻 璃 Diamond 鑽石

124

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sin

−1

Critical angle

2.4 Total internal reflection (SB p.69)

Class Practice 4: A light ray travels from water to air. Describe the changes in the brightness of the refracted ray and the reflected ray when the angle of incidence (i) increases from 0º to 60º. The critical angle of water is 48.8º. a weak reflected ray and a strong refracted ray are observed.

When 0º < i < 48.8 º, _____________________________. a strong reflected ray appears and a weak refracted ray emerges along the water-air boundary. When i = 48.8 º, __________________________________. the light ray is totally reflected at the water-air boundary and theAnswer reflected！ When i > 48.8 º, __________________________________. answer now!! ray becomes as bright asClick thefor incident ray. No refracted ray is observed. 125

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2.4 Total internal reflection (SB p.69)

Critical angle

Class Practice 5: Referring to the following figure, comment Total on theinternal following statement: reflection does not occur “Since because the angleairofisincidence is greater the critical optically (60º) less dense thanthan glass. angle Total of glass (41.8º), total internal reflection will occur.” internal reflection only occurs when light Is this statement correct? briefly. travels from anExplain optically denser medium to an optically less dense one.

air

Answer!

glass

Click for answer now!!

126

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2.4 Total internal reflection (SB p.70)

Examples of total internal reflection

Examples of total internal reflection 1. Sparkle of diamond o Reason: angle of diamond (24than ) Why is Critical diamond more brilliant glass?

<< Critical angle of glass (42o ) Light rays enter the diamond from Amount of light that undergoes total internal reflection above inside diamond is greater • undergo total internal reflection at the bottom • emerge from the top surface

give brilliant colour diamond

air

127

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2.4 Total internal reflection (SB p.70)

Examples of total internal reflection

2. Mirage Why is there a mirage?

128

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2.4 Total internal reflection (SB p.71)

Examples of total internal reflection

Reason: Light rays enter from cold air to hot air (different media), then refraction and total internal reflection (at A) occur. eye of the observer cold air

hot air

total internal reflection

129

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2.4 Total internal reflection (SB p.72)

Examples of total internal reflection

3. Scene under water Can the diver see the object behind the barrier? Yes, because light rays undergo total internal reflection on the water surface

130

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2.4 Total internal reflection (SB p.72)

Applications of total internal reflection

Experiment 2D: Construction of a prismatic periscope Expt. VCD

131

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2.4 Total internal reflection (SB p.72)

Applications of total internal reflection

Applications of total internal reflection 1. Prismatic periscope

• Principle — i (45o) > cg (42o) — total internal reflection

• Nature of image — erect — same size as the object 132

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2.4 Total internal reflection (SB p.74)

Applications of total internal reflection

Class Practice 6: Is the image formed by a periscope real or virtual? Complete the following ray diagram and answer the question. object object

Answer! Click for answer now!!

image

The image formed by a periscope is 133

virtual

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.

2.4 Total internal reflection (SB p.75)

Applications of total internal reflection

2. Binoculars — see distant objects — two prisms inside prism

light ray

134

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2.4 Total internal reflection (SB p.76)

Applications of total internal reflection

3. Optical fibres for telecommunication — light ray undergoes total internal reflection at the core-cladding interface total internal reflection cladding

core light ray

135

a light ray emerges at the opposite end of the optical fibre

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2.4 Total internal reflection (SB p.76)

Applications of total internal reflection

Reasons for using optical fibres instead of copper cables • thinner, lighter and cheaper • provide a higher bandwidth and carry more telephone calls at a time • avoid electrical interference and more secured • loss of signals is minimized

136

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2.4 Total internal reflection (SB p.77)

Applications of total internal reflection

4. Optical fibres for endoscope — doctors use it to examine the internal organs of patients light illuminates the internal organs of the body

endoscope light is reflected back to the detector and is analysed by doctors 137

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2.4 Total internal reflection (SB p.78)

5. Fish-eye view

Applications of total internal reflection

— light rays from the water surface below undergo total internal reflection on the water surface View of fish-eye is restricted within an angle of 97.6°

48.8º

138

48.8º

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Chapter 3 Lenses 3.1 Cylindrical and Spherical Lenses 3.2 Construction Rules for Images Formed by Lenses 3.3 Formation of Images by Lenses Manhattan Press (H.K.) Ltd. © 2001

Section 3.1

Cylindrical and Spherical Lenses • Terminology for lenses

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3.1 Cylindrical and spherical lenses (SB p.88)

Lenses — Made of transparent materials — Light rays are refracted when passing through a lens

141

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3.1 Cylindrical and spherical lenses (SB p.88)

— with cylindrical surfaces spherical lenses — with spherical surfaces cylindrical lenses

Lenses

cylindrical lenses

142

spherical lenses

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3.1 Cylindrical and spherical lenses (SB p.89)

Lenses

convex lenses — the thickest at centre concave lenses — the thinnest at centre

the thickest at centres of convex lenses

143

the thinnest at centres of concave lenses

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3.1 Cylindrical and spherical lenses (SB p.89)

Lenses

convex lenses — the thickest at centre concave lenses — the thinnest at centre

spherical convex lens

cylindrical convex lens

cylindrical concave lens

144

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spherical concave lens

3.1 Cylindrical and spherical lenses (SB p.89)

When parallel light rays pass through a convex lens — emerging rays converge — converging lens concave lens —

145

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3.1 Cylindrical and spherical lenses (SB p.89)

When parallel light rays pass through a convex lens —

converging lens

concave lens — emerging rays diverge — diverging lens

146

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Terminology for lenses

3.1 Cylindrical and spherical lenses (SB p.89)

Terminology for lenses 1. Principal axis 2. Optical centre (C) convex lens

concave lens principal axis

optical centre

147

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3.1 Cylindrical and spherical lenses (SB p.90)

Terminology for lenses

Experiment 3A: Refraction of light by convex and concave lenses Expt. VCD

148

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3.1 Cylindrical and spherical lenses (SB p.91)

Terminology for lenses

When parallel light rays pass through a convex lens — emerging rays converge to a point : principal focus or focus (F) concave lens convex lens

focus

149

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3.1 Cylindrical and spherical lenses (SB p.91)

Terminology for lenses

When parallel light rays pass through a convex lens — emerging rays converge to a point concave lens — emerging rays diverge, extended backwards to meet a point : focus (F) concave lens

focus

Note: Light rays can be directed towards a lens from either side, so a lens has two foci. 150

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3.1 Cylindrical and spherical lenses (SB p.91)

Terminology for lenses

Focal plane — a plane passing through F and perpendicular to principal axis Focal length (f) — distance between F and C

principal axis

focal plane

Note: If the incoming parallel focal light planerays are not parallel to the principal axis, the refracted rays converge on the focal plane. 151

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3.1 Cylindrical and spherical lenses (SB p.91)

Greater curvature of lens (shorter focal length)

smaller curvature

Light rays converges more (θ 2 > θ 1) greater curvature

θ

152

Terminology for lenses

θ

1

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2

Section 3.2

Construction Rules for Images Formed by Lenses • Construction rules for images formed by convex lens • Construction rules for images formed by concave Manhattan Press (H.K.) Ltd. © 2001

3.2 Construction rules for images formed by lenses (SB p.92)

Graphical symbols convex lens

154

concave lens

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3.2 Construction rules for images formed by lenses (SB p.92) Construction rules for images formed by convex lens

Construction rules for images formed by convex lens 1. Parallel to the principal axis

　

passes through F on the opposite side of the incident ray

F

155

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3.2 Construction rules for images formed by lenses (SB p.93) Construction rules for images formed by convex lens

Construction rules for images formed by convex lens 2. Towards F 　

parallel to the principal axis

F F

156

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3.2 Construction rules for images formed by lenses (SB p.93) Construction rules for images formed by convex lens

Construction rules for images formed by convex lens 3. Towards C 　

157

passes through C without deviation

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3.2 Construction rules for images formed by lenses (SB p.93) Construction rules for images formed by convex lens

Principle of reversibility of light

The refraction of ray 2 is the reverse of ray 1 Reason: The principle of reversibility of light ray 1

158

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ray 2

3.2 Construction rules for images formed by lenses (SB p.94) Construction rules for images formed by convex lens

Class Practice 1 : Referring to the figure below, an image I is formed when an object is placed on the left hand side of a convex lens. Draw two light rays to locate the position of the object as O.

159

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Ans wer

3.2 Construction rules for images formed by lenses (SB p.95) Construction rules for images formed by concave lens

Construction rules for images formed by concave lens 1. Parallel to the principal axis

　

appears to come from F on the same side of the incident ray

F

160

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3.2 Construction rules for images formed by lenses (SB p.94) Construction rules for images formed by concave lens

Construction rules for images formed by concave lens 2. Towards F 　

parallel to the principal axis

F

161

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3.2 Construction rules for images formed by lenses (SB p.95) Construction rules for images formed by concave lens

Construction rules for images formed by concave lens 3. Towards C 　

passes through C without deviation

| c

162

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3.2 Construction rules for images formed by lenses (SB p.97) Construction rules for images formed by concave lens Class Practice 2 ：

Draw the refracted ray in each of the following figures. (a)

(b)

163

Ans wer

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Section 3.3

Formation of Images by Lenses • Locate the images by graphical method • Image nature of lenses • Finding the focal length of a convex Manhattan Press (H.K.) Ltd. © 2001 lens

3.3 Formation of images by lenses (SB p.97)

Experiment 3B: Formation of image by convex and concave lenses

Expt. VCD

165

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Locate the images by graphical method

3.3 Formation of images by lenses (SB p.98)

Locate the images formed by convex lens by graphical method

1. Draw an arrow (object) O

2. Draw two special light rays from the tip I principal of the object axis 3. Draw the refracted rays to meet at a point convex 4. Draw an arrow lens (image) to the Note: Image nature of convex lens principal axis — changes with object distance 166

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Locate the images by graphical method

3.3 Formation of images by lenses (SB p.98)

Locate the images formed by concave lens by graphical method 1. Draw an arrow (object)

2. Draw two special light rays from the tip of the object 3. Extend the refracted ray backwards to meet at a point 4. Draw an arrow (image) to the principal axis

O

I Note: Virtual images cannot be formed on the screen, you observe them by looking into concave lens the mirrors directly. 167

Note: nature of images formed by a concave lens — erect, virtual and diminished

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3.3 Formation of images by lenses (SB p.98)

Height of image (hi)

Magnification (m) =

=

Height of object (ho) Image distance (v) Object distance (u) ho

ho

Locate the images by graphical method

principal axis

hi

hi

concave lens

convex lens 168

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3.3 Formation of images by lenses (SB p.99)

Image nature of lenses

Image nature of convex lens 1. Object is placed between C and F I

o

image

169

• Image is formed on the same side as the object • Nature of image — virtual — erect — magnified (m > 1)

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3.3 Formation of images by lenses (SB p.99)

Image nature of lenses

Image nature of convex lens 2. Object is placed at F o

170

• Image is formed at infinity • Nature of image — cannot be determined Manhattan Press (H.K.) Ltd. © 2001

3.3 Formation of images by lenses (SB p.99)

Image nature of lenses

Image nature of convex lens 3. Object is placed between F and 2F • Image is formed beyond 2F on the opposite side of I the lens • Nature of image object — real — inverted — magnified (m > 1) image

o

171

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3.3 Formation of images by lenses (SB p.99)

Image nature of lenses

Image nature of convex lens 4. Object is placed at 2F o I

object

• Image is formed at 2F on the opposite side of the lens • Nature of image — real — inverted — same size as object (m = 1)

image 172

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3.3 Formation of images by lenses (SB p.100)

Image nature of lenses

Image nature of convex lens

5. Object is placed beyond 2F

o

object

• Image is formed between F and 2F on the opposite side of the lens • Nature of image — real — inverted — diminished (m < 1)

image 173

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3.3 Formation of images by lenses (SB p.100)

Image nature of lenses

Image nature of convex lens 6. Object is placed at infinity

image

174

• Image is formed on the focal plane • Nature of image — real — inverted — diminished (m < 1)

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3.3 Formation of images by lenses (SB p.101)

Image nature of lenses

Class Practice 3 ： In the following figure, sketch the refracted rays and locate the image (I). I

Ans wer 175

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3.3 Formation of images by lenses (SB p.102)

Image nature of lenses

Class Practice 4 ： An object (letter “P” card) which is 5 cm in height, is placed at 30 cm in front of a convex lens. A clear image is formed on the screen. The focal length of the lens is 20 cm. convex lens

translucent screen

(a) Is the image real or virtual?

The image is real.

176

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Ans wer

3.3 Formation of images by lenses (SB p.102)

Image nature of lenses

Class Practice 4 (Cont’d): (b) When a boy is at position (i) X and then (ii) Y, what will he see? b (i) If the boy is at position X, he will see a letter _______.

　　　 letter

d (ii) If the boy is at position Y, he will see a

convex _______. lens

translucent screen

Ans wer 177

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3.3 Formation of images by lenses (SB p.102)

Image nature of lenses

Class Practice 4 (Cont’d) ： (c) Draw a ray diagram to determine the image distance and magnification. Use the scale shown in the figure.

6x 10

60 cm

Image distance Height = __________ = __________. of

　　　

image

1 0 5

Height of Magnification ＝object ─────＝────＝ 178

Ans wer

2

_______. 　

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3.3 Formation of images by lenses (SB p.103)

Image nature of lenses

Image nature of concave lens

Object is placed at any position

• Image is formed between F and C,and on the same side as the object

o I

• Nature of image image object

Note: When the object is placed at infinity, the image is formed on the 179

focal plane.

— virtual — erect — diminished (m < 1)

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3.3 Formation of images by lenses (SB p.103)

Image nature of lenses

Focal length of concave lens is fixed, Shorter object distance

longer object distance

180

larger image, but must be smaller than the object (m < 1)

shorter object distance

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3.3 Formation of images by lenses (SB p.104)

Image nature of lenses

Class Practice 5 ： An object O is placed in front of a concave lens. Three light rays, p, q and r are directed towards the concave lens as shown in the following figure.

(a) Sketch the refracted rays of p, q and r. (b) Locate the image I.

181

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Ans wer

3.3 Formation of images by lenses (SB p.104)

Image nature of lenses

Class Practice 6 ： The following figures show the images formed by two lenses, L1 and L2. Name the lenses.

lens L1

lens L2

conc con ave vex L1 is a __________ lens, and L2 is a __________ lens.

182

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Ans wer

3.3 Formation of images by lenses (SB p.105)

Image nature of lenses

Class Practice 7 ： An object O, which is 15 cm in height, is placed at 30 cm in front of a concave lens. The focal length of the lens is 15 cm.

(a) Draw a ray diagram to locate the image I. Use the scale shown in the figure.

Ans wer

183

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3.3 Formation of images by lenses (SB p.105)

Image nature of lenses

Class Practice 7(Cont’d): (b) State the nature of the image. 　

The image is virtual, erect and diminished.

Ans wer

184

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3.3 Formation of images by lenses (SB p.105)

Finding the focal length of a convex lens

Experiment 3C ： Finding the focal length of a convex lens Expt. VCD

185

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3.3 Formation of images by lenses (SB p.106)

Finding the focal length of a convex lens

Finding the focal length of a convex lens

Convex lenses converge parallel light rays on the focal plane parallel light rays

Image distance = Focal length of convex lens focal plane

principal axis

focal length (f )

186

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3.3 Formation of images by lenses (SB p.106)

Finding the focal length of length of a a convex lens

Alternative method to find the focal convex lens (plane mirror method) Object is placed at F — light rays are parallel after passing through the lens — then reflected back along their original paths when hitting plane mirror — image is formed on the screen after passing through the lens again — image distance = object distance = focal length convex lens

convex lens image

object

object plane mirror plane mirror 187

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Chapter 4 Optical Instruments 4.1 Magnifying Glass 4.2 Human Eye 4.3 Camera

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Section 4.1

Magnifying Glass

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4.1 Magnifying glass (SB p.114)

What is a magnifying glass? It is a convex lens with a short focal length

190

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4.1 Magnifying glass (SB p.115)

Properties of a magnifying glass (convex lens)

• Object is placed I

— within the focal length • Nature of image — virtual, erect and magnified

191

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4.1 Magnifying glass (SB p.115)

When focal length of a magnifying glass is fixed, longer object distance larger magnification shorter object distance

I

I

192

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longer object distance

4.1 Magnifying glass (SB p.116)

When object distance is fixed, thicker convex lens (shorter focal length)

I

193

longer focal length

larger magnification

I

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shorter focal length

4.1 Magnifying glass (SB p.117)

Class Practice 1 ： An object is placed in front of a magnifying glass at different positions as shown in the figure below. Locate the images for the object at u1, u2 and u3. I2

I1

I3

Ans wer 194

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4.1 Magnifying glass (SB p.118)

Class Practice 1 (Cont’d) I2

I1

I3

When the object is moved from u1 to u2, the image larger

erect

becomes ______________ in size, but it is still _______________ and virtual. Ifmagnified the object is moved inverted real Ans to u3, the image will become ____________, ____________ and ____________. 195

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wer

4.1 Magnifying glass (SB p.118)

Class Practice 2: A boy places a magnifying glass 3 cm above a book. He looks at a word on the book through the lens. beneath

The image formed is _____________ (above / beneath) the lens.

The boy raises the lens until the word is located abovejust beyond the focus of the lens. The new image formed Ans is ___________ (above / beneath) the lens.wer 196

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Section 4.2 Human Eye • • • •

Structure of human eye Control of brightness Accommodation Defects of vision Manhattan Press (H.K.) Ltd. © 2001

Structure of human eye

4.2 Human eye (SB p.118)

Human eye — Optical instrument inside our bodies — Focus objects, perceive depths, distinguish colours

198

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Structure of human eye

4.2 Human eye (SB p.118)

Structure of human eye (1) cornea control size (2) pupil of pupil (3) iris iris (4) lens pupil light (5) ciliary muscles rays (6) retina cornea (7) optic nerve

image formed on it retina optic nerve

ciliary muscles

Note: Images formed on the retina are real and inverted. 199

control thickness of lens

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lens

transmit signals to brain

Control of brightness

4.2 Human eye (SB p.119)

Control of brightness — depends on the size of pupil In bright environment, — iris reduces the size of pupil — limit the amount of light entering the eye

size of pupil reduces 200

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Control of brightness

4.2 Human eye (SB p.119)

In dim environment, — —

size of pupil widens increase the amount of light entering the eye

size of pupil widens 201

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Control of brightness

4.2 Human eye (SB p.119)

Colour of the eye — colour of the iris

202

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Accommodation

4.2 Human eye (SB p.120)

Accommodation — depends on thickness of lens Looking at a distant object — Ciliary muscles relax — Lens becomes thinner (longer focal length)

Note: Distance between lens and retina = Focal length of lens 203

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Accommodation

4.2 Human eye (SB p.120)

Looking at a near object — Ciliary muscles contract — Lens becomes thicker (shorter focal length)

204

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Accommodation

4.2 Human eye (SB p.120)

Accommodation — See objects at different distances — Ciliary muscles change the lens shape — Focus images on the retina light from distant object

205

light from near object

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Defects of vision

4.2 Human eye (SB p.120)

Range of vision the farthest point that an eye can see clearly (infinity) Near point — the nearest point that an eye can see clearly (25 cm) Far point —

far point

infinity

near point

25 cm

Note: The range of vision for a normal eye is from about 25 cm to infinity. 206

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Defects of vision

4.2 Human eye (SB p.121)

Experiment 4A: Model eye kit experiment

Expt. VCD

207

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Defects of vision

4.2 Human eye (SB p.122)

Short-sightedness • Cannot see distant objects clearly • Cause — the eyeball is too long •

or the lens is too thick Effect — image is formed in front of the retina image formed in front of the retina light rays from distant object

Note: Near point < 25 cm (short-sighted eye) 208

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Defects of vision

4.2 Human eye (SB p.122)

Correction of a short-sighted eye — Wear spectacles with concave lenses light rays appear to come from a nearer point

light rays from distant object

concave lens

209

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Defects of vision

4.2 Human eye (SB p.122)

Long-sightedness • Cannot see near objects clearly • Cause — the eyeball is too short •

or the lens is too thin Effect — image is formed behind the retina image formed behind the retina

light rays from near object

210

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Defects of vision

4.2 Human eye (SB p.123)

Correction of a long-sighted eye — Wear spectacles with convex lenses convex lens light rays from near object

light rays appear to come from a farther point

211

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Defects of vision

4.2 Human eye (SB p.123)

Class Practice 3: Chris is suffering from shortsightedness. What kind of spectacles should he wear? He should wear a pair of spectacles with concave lenses.

Chris is now looking at a distant object. Draw on the following figure to show (i) how the light rays from the distant object travel inside the eyeball without spectacles, and (ii) how the eye defect can be corrected with the spectacles.

Ans wer

concave lens 212

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Defects of vision

4.2 Human eye (SB p.124)

Class Practice 4: A short-sighted person is looking at a near object in front of him. Draw in the following figure to show the refraction of the two light rays by his eye lens.

light rays from near object

on the retina

The image is formed _________________. 213

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Ans wer

Defects of vision

4.2 Human eye (SB p.124)

Astigmatism • Form distorted images • Cause — asymmetry of cornea shape • Correction — wear a non-spherical lens

Look at this set of lines to check whether you are suffering from astigmatism 214

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Section 4.3

Camera • Structure of camera • Factors affecting the amount of light entering a camera • Focusing Manhattan Press (H.K.) Ltd. © 2001

Structure of camera

4.3 Camera (SB p.125)

Camera — functions like a human eye (1) lens (2) aperture (3) film (4) focusing ring (5) shutter adjusts the amount of light entering the camera

image formed on the film

film aperture

lens

focusing ring

Note: The image formed on the film is inverted and real. 216

shutter

controls the exposure time of the film to light plastic covered with light sensitive chemical

adjusts the distance between lens and film

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focuses incoming light onto the film

4.3 Camera (SB p.126)

Control the amount of light entering a camera

Factors affecting the amount of light entering a camera

(1) Size of aperture (2) Shutter speed

(1) Size of aperture — Controlled by a diaphragm (metal sheets) — Control the intensity of light onto the film aperture

diaphragm 217

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4.3 Camera (SB p.127)

Control the amount of light entering a camera

Factors affecting the amount of light entering a camera

(1) Size of aperture (2) Shutter speed

(2) Shutter speed — Open and closure of shutter depend on the chosen speed — Control the exposure time of the film to light

218

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Focusing

4.3 Camera (SB p.127)

Focusing film focusing ring object

• Properties — lens is mounted on the focusing ring

image

lens

• Different object distance

Note: The process of adjusting — adjust the lens-to-film distance the lens-to-film distance is called (image distance) focusing. — focus images on the film 219

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Focusing

4.3 Camera (SB p.127)

Focusing a far object — Move lens close to the film (reduce image distance) object

image lens

220

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Focusing

4.3 Camera (SB p.128)

Focusing a near object — Moved lens away from the film (increase image distance) object image

221

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Chapter 5 Temperature, Heat and Internal Energy

5.1 Temperature

5.2 Thermometers 5.3 Heat and Internal Energy 5.4 Specific Heat Capacity and Energy Transfer in Mixing Process Manhattan Press (H.K.) Ltd. © 2001

Section 5.1 Temperature • Temperature scale

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5.1 Temperature (SB p.140)

What is “temperature”?

• It tells how hot or cold an object is • A hot body has a higher temperature than a cold one

224

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Temperature scale

5.1 Temperature (SB p.140)

Cold?

• Different people have their own sensation of hotness. • An objective scale is established to measure the temperature accurately

Hot?

Temperature scale is the objective scale 225

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Temperature scale

5.1 Temperature (SB p.141)

Celsius scale • In Hong Kong, the most common temperature scale is Celsius scale • It was introduced by a Swedish astronomer, called Anders Celsius, in 1742

226

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Temperature scale

5.1 Temperature (SB p.142)

Celsius scale

Lower fixed point (or ice point) — 0 ºC, temperature for

upper fixed point

pure ice to melt at normal atmospheric pressure

lower fixed point boiling water

melting ice

Upper fixed point (or steam point) — 100 ºC, temperature of the steam over pure boiling water at normal atmospheric pressure

Calibration — divide the included region equally into 100 divisions

227

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Temperature scale

5.1 Temperature (SB p.141)

Fahrenheit scale Often used in hospitals and clinics to indicate the • 1. body temperature • 2.

The melting point of ice is 32ºF

• 3.

The steam point of boiling water is 212ºF

• 4.

The normal body temperature is 98.6ºF

228

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Section 5.2

Thermometers • Liquid-in glass thermometers

• Other thermometers Manhattan Press (H.K.) Ltd. © 2001

5.2 Thermometers (SB p.142)

How do you know about “thermometers”? Uses Material s

230

measure temperature substance that has the property varies linearly with the temperature Manhattan Press (H.K.) Ltd. © 2001

5.2 Thermometers (SB p.142)

Thermometer is a tool for measuring temperature • Sensing property •Property that varies linearly with temperature: • Length • Colour • Electrical conductivity

231

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5.2 Thermometers (SB p.146)

Other thermometers

Types of thermometers • Liquid-in-glass thermometer • Platinum resistance thermometer • Rotary thermometer • Thermochromic thermometer

232

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5.2 Thermometers (SB p.142)

Liquid-in-glass thermometers

Liquid-in-glass thermometers

Liquids in the capillary glass tube expands or contracts linearly with temperature changes 233

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5.2 Thermometers (SB p.143)

Liquid-in-glass thermometers

Comparison of two liquid-in-glass thermometers Mercury-in-glass thermometer

Alcohol-in-glass thermometer

quick response to the change slow response in temperature can measure high can measure low temperature (down to temperature (up to 357°C) −110°C) mercury is poisonous, avoid alcohol is non-poisonous, but inhaling its vapour once the flammable, widely used in thermometer is broken school laboratories no need to dye the liquid alcohol is colourless, it is dyed red for easier observation more expensive cheaper 234

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Liquid-in-glass thermometers

5.2 Thermometers (SB p.143)

Clinical thermometers

Constriction — prevents the mercury from falling back to the bulb, so as to maintain the highest temperature reading 235

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Liquid-in-glass thermometers Class Practice 1: A liquid-in-glass thermometer

5.2 Thermometers (SB p.146)

has column heights of 2.5 cm and 14 cm at ice point and steam point respectively. After immersing the thermometer into an unknown liquid, the liquid column height becomes 9 cm. Find the temperature of the liquid the unknown be T. statetemperature the assumption you have made. •Let and 9 – 2.5 ) T ( 　　　　　　　 = ( 　　　　　　 ) ( 　　　　　　　 ) 100 14 – 2.5 56.5°C T = 　　　　　　　 •The equation is based on the assumption that the liquid expands 　　　　　　　 　　　 with the temperature increase. linearly

236

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Ans wer

5.2 Thermometers (SB p.146)

Other thermometers

Platinum resistance thermometer •Property — –resistance increases when the temperature rises

•Method — –measure the resistance of a platinum wire that is in contact with the object

•Temperature range — ––200ºC to 1 000ºC 237

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Other thermometers

5.2 Thermometers (SB p.146)

Rotary thermometer rivet

At higher temperature:

copper iron copper iron

238

• Bimetallic strip • — made up of two different metal strips • — when temperature rises, one of the metal strips expands more • — metal strips bends

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Other thermometers

5.2 Thermometers (SB p.147)

Rotary thermometer •Property — –consists of a coiled bimetallic strip which bends when temperature rises •Method — –the strip coils up and moves the pointer to indicate the temperature •Application — –measure the temperatures in ovens and refrigerators 239

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Other thermometers

5.2 Thermometers (SB p.147)

Thermochromic thermometer •Property — –colour changes with temperature •Method — –make use of colour to indicate the temperature •Temperature range — –20ºC to 40ºC •Application — –measure the temperatures of body and water inside a fish tank 240

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Section 5.3

Heat and Internal Energy • Heat

• Internal energy

• Power

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Heat

5.3 Heat and internal energy (SB p.148)

Thermal equilibrium If TA > TB ， energy transfers from A to B

If TA = TB ， no energy transfers and thermal equilibrium attains

After certain time

energy transfers from A to B 242

no energy transfers

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5.3 Heat and internal energy (SB p.148)

Heat

Law of conservation of energy •It states that in all energy transformation processes, energy cannot be created or destroyed. •But energy can • transfer from one body to another • change from one form to another 243

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5.3 Heat and internal energy (SB p.149)

Heat • Heat is defined as the energy transferred between two bodies of different temperatures

244

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Heat

Internal energy

5.3 Heat and internal energy (SB p.149)

Internal energy •Internal energy = Kinetic energy + Potential energy originated from motion of the molecules

245

originated from bonding between molecules

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Internal energy

5.3 Heat and internal energy (SB p.150)

Intermolecular bonding sphere kinetic energy

spring potential energy

•The bond between two molecules is regarded as the spring linking two metal spheres 246

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5.3 Heat and internal energy (SB p.150)

Internal energy

Temperature rises, kinetic energy increases

• When temperature rises ∀ → molecules vibrate more vigorously ∀ → kinetic energy increases

247

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5.3 Heat and internal energy (SB p.150)

Internal energy

State changes, potential energy changes • Weak bonds • are formed from the intermolecular attractions between molecules • are independent of temperature

248

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5.3 Heat and internal energy (SB p.151)

Power Energy • Power = ——— Time E • P = —— t • 1 W = 1 J s–1 A heater rated 50 W means •e.g. 50 J of energy is transferred in 1 second • 249

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Power

Section 5.4

Specific Heat Capacity and Energy Transfer in Mixing Process • Heat capacity • Specific heat capacity • Energy transfer in mixing process Manhattan Press (H.K.) Ltd. © 2001

5.4 Specific heat capacity and energy transfer in mixing process (SB p.152)

Heat capacity

Heat capacity

•For the same amount of energy absorbed, different bodies have different temperature changes. We use heat capacity (C) to describe this property. temperature rises by 1ºC energy

heat capacity = energy 251

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.152)

Calculate heat capacity

Heat capacity

Assume the temperature of body rises from T1 to T2 after it has absorbed an amount of energy E, the heat capacity of the body can be found by: Heat capacity =

Energy transfer

Temperaturechanges

i.e. C= 252

E

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T -T

5.4 Specific heat capacity and energy transfer in mixing process (SB p.152) Heat capacity

Class Practice 2 (a) Two substances are heated under •(a) the same physical condition and their temperature changes against time are plotted in the graph:

Temperature / ºC

smaller

•Substance A has a ˍˍˍˍ temperature change than substance B. Therefore, substance A has a higher ˍˍˍˍ heat capacity than substance B. 253

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su

e c n a bs t

B

ce A n a t s b su

Time / s

Ans wer

5.4 Specific heat capacity and energy transfer in mixing process (SB p.153) Heat capacity

Class Practice 2 (Cont’d)

•(b) In a heating process, the temperature of an object rises from 22 ºC to 95 ºC. If the heat capacity of the

Temperature / ºC

object is 900 J ºC-1 , ˍˍˍˍ 65 700 J of heat is absorbed by the object. Once the heat is absorbed, it becomes the internalenergy of the object. ˍˍˍˍ

su

B e c an t s b

nc substa

eA

Time / s

Ans wer 254

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.153)

Comparison of heat capacity

Heat capacity

• An object with a higher heat capacity means that more energy is needed to raise its temperature • Since the aluminium rod has a higher heat capacity than that of the copper rod, its temperature rise is smaller when same amount of energy is provided 255

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.153) Heat capacity

copper rod

heat

The more the energy absorbed by the copper rod

Temperature rise will be greater 256

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.153) Heat capacity

aluminium rod use aluminium rod instead of copper rod heat （ provide same amount of energy ）

Since the heat capacity of aluminium rod is higher, the temperature rise is smaller than that of copper rod 257

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.153)

Specific heat capacity

Specific heat capacity

• 1. Same mass of copper and aluminium have different heat capacity • 2. To compare the heat capacities of different bodies, apart from their masses, types of substances also need to be considered. • 3. Specific heat capacity (c) of a substance is the heat required to raise the temperature of 1 kg of the substance by 1 ºC

258

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.153)

Absorption of specific heatSpecific heat capacity capacity •e.g. •specific heat capacity of water is 4 200 J kg–1 ºC–1

1 kg water

4 200 J

259

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temperature increases by 1ºC

5.4 Specific heat capacity and energy transfer in mixing process (SB p.153) Specific heat capacity

Release of specific heat capacity

1 kg water

Conversely, 4 200 J

260

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temperature decreases by 1ºC

5.4 Specific heat capacity and energy transfer in mixing process (SB p.154) Specific heat capacity

Experiment 5A Specific heat capacity of water

Intro. VCD

Expt. VCD

261

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.154) Specific heat capacity

Experiment 5A

• Energy (E) transfers from joulemeter to water is (Ef – Ei) • Temperature rise (∆ T) of water is (Tf – Ti) ∆

262

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.155) Specific heat capacity

Experiment 5A Methods to minimize errors

Regarding polystyrene cup, • heat absorbed by it is very small • poor conductor of heat • →reduce heat loss to the surroundings •

263

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.155) Specific heat capacity

Experiment 5A Methods to minimize errors

Polystyrene cup lid : • can evaporation of water • can reduce heat loss

•

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.155) Specific heat capacity

Experiment 5A Methods to minimize errors

•The water should be well stirred throughout the process to ensure the water is being heated uniformly

265

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.155) Specific heat capacity

Experiment 5A Methods to minimize errors

•When the heater is switched off, its temperature is still higher than that of the water •→ Wait for steady reading 266

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.157) Specific heat capacity

Class Practice 3: A heater of power 200 W is used to heat up a liquid of mass 0.5 kg. The following graph shows the temperature-time relation. (a) Determine the room temperature. The room temperature is 24ºC ˍˍˍˍˍˍˍˍ .

Temperature / ºC

(b) How much energy is supplied by the heater in the heating process? E P= t , By the equation 200 × 80 E = P × t = ˍˍˍˍˍˍ 16 000 J =ˍˍˍˍˍˍˍˍ . 267

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Ans wer Time / s

5.4 Specific heat capacity and energy transfer in mixing process (SB p.158) Specific heat capacity

Class Practice 3 (Cont’d)

Temperature/ºC

• (c) Find the specific heat capacity of the liquid. E c= m∆ T ( 　 16 　 000 　 　) 　 = 0.5　 　)( 　56 24　) 　 (　　 　–　 1 000 J kg–1 ºC–1 = ˍˍˍˍˍˍˍˍˍˍ 268

Ans wer Manhattan Press (H.K.) Ltd. © 2001

Time/s

5.4 Specific heat capacity and energy transfer in mixing process (SB p.158) Energy transfer in mixing process

Experiment 5B Mixture of hot and cold water Expt. VCD

269

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.159) Energy transfer in mixing process

Experiment 5B hot water (temperature TA)

Ａ

cold water (temperature TB)

Ｂ

Energy released by Energy absorbed by hot water: cold water: EA = mA c (TA – Tf) EB = mB c (Tf – TB)

270

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mixture (temperature Tf)

5.4 Specific heat capacity and energy transfer in mixing process (SB p.159) Energy transfer in mixing process

Experiment 5B

Assume there is no heat loss to the surroundings during mixing

271

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Class Practice 4: A student tries to find the specific

beaker A

heat capacity by the method of mixing. He heats a copper block of mass 0.6 kg in a beaker containing boiling water (left). After a while, he quickly immerses the block in another beaker which contains 1 kg of water at 25 °C (right). After gentle stirring, he finds that the final temperature of the water is 29 °C . Given the specific heat (a) Find the heat gained by the water in beaker •–1 capacity of water is 4 200 J kg B.°C–1 . 0.6 kg copper block

boiling water

•

The heat gained by the water in beaker B

＝ mc∆ T • ＝ ˍˍˍˍˍˍˍˍˍ • beaker ＝ ˍˍˍˍˍˍˍˍˍ •

B

272

Ans wer

1 kg water at 25 °C Manhattan Press (H.K.) Ltd. © 2001

1 × 4 200 × (29 – 25)

16 800 J

5.4 Specific heat capacity and energy transfer in mixing process (SB p.161) Energy transfer in mixing process

Class Practice 4 (Cont’d) • (b) Assume there is no heat loss. What is the specific heat capacity of copper? • The heat lost16by800the J copper (E) = The heat gained by the water in beaker B = ˍˍˍˍˍˍ 100ºC • In the figure on theEleft, the copper block is = heated to a temperature m∆Tof ˍˍˍˍˍˍ. ( 　　　　　　　　　　 ) 　　 16 800 • Specific heat capacity = (c) 0.6 × (100 – ( 　　　　　　　　　　 ) 　　 Ans wer

273

= __________ 29) _____ –1 –1

394 J kg ºC

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.162) Effects of high specific heat capacity of water

Water as coolant

•As water has a high specific heat capacity,it absorbs a large amount of heat

274

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.162) Effects of high specific heat capacity of water

Damping effect on climate

Coastal area: Temperature difference between daytime and night-time, and in different seasons is smaller •Since sea water has a higher specific heat capacity than the land, the temperature changes at a slower rate

Inland area : Temperature difference between daytime and night-time, and in different seasons is greater 275

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5.4 Specific heat capacity and energy transfer in mixing process (SB p.162) Effects of high specific heat capacity of water

Regulation of body temperature

• Our bodies store a large amount of water • Water has a high specific heat capacity • →The body temperature can be kept steady even when there is a sudden temperature change

276

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Chapter 6 Change of State 6.1 Three states of Matter 6.2 Cooling Curve of a Substance 6.3 Specific Latent Heat of Fusion 6.4 Specific Latent Heat of Vaporization Manhattan Press (H.K.) Ltd. © 2001

Section 6.1

• Three States of Matter

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6.1 Three states of matter (SB p.171)

Matter has three physical states: solid, solid liquid and gas

gas

solid

279

liquid

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6.1 Three states of matter (SB p.171)

Change of state

•Change of state — •Under certain conditions (specific pressures and temperatures), a substance can change from one state to another

280

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6.1 Three states of matter (SB p.172)

Fusion

water melting point (0ºC)

ice 281

•Fusion — •A substance changes from solid state to liquid state •Melting point — Temperature that starts to melt •The melting point of ice is 0ºC Manhattan Press (H.K.) Ltd. © 2001

6.1 Three states of matter (SB p.172)

Solidification

water freezing point (0ºC)

ice 282

•Solidification — •A substance changes from a liquid state to a solid state •Freezing point — •Temperature that starts to solidify •The freezing point of water is 0ºC

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6.1 Three states of matter (SB p.172)

Melting point and freezing point

water freezing point (0ºC)

melting point (0ºC)

•Under normal atmospheric conditions, the melting point and the freezing point of a particular substance is the same

ice 283

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6.1 Three states of matter (SB p.172)

Vaporization and condensation

vaporization (100ºC)

steam

condensation (100ºC)

•Vaporization — •A liquid changes to a gas •Condensation — •A gas changes to a liquid •Under normal atmospheric conditions, the boiling point and the condensation point are the same

water

284

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Section 6.2 Cooling Curve of a Substance • Cooling curve of octadecan1-ol • Explanation of the cooling curve Manhattan Press (H.K.) Ltd. © 2001

6.2 Cooling curve of a substance (SB p.173) Cooling curve of octadecan-1-ol

Experiment 6A Cooling curve of octadecan-1-ol

Intro. VCD

Expt. VCD

286

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6.2 Cooling curve of a substance (SB p.174) Cooling curve of octadecan-1-ol

Cooling curve of octadecan-1-ol consists of three regions Temperature/ ºC

region A (liquid)

• • •

In region A, — octadecan-1-ol exists in liquid state — since its temperature is higher than the room temperature (about 25ºC), heat flows from it to the surroundings, it cools gradually

region B (solid + liquid)

region C (solid)

Time/ minutes

287

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6.2 Cooling curve of a substance (SB p.174) Cooling curve of octadecan-1-ol

Temperature / ºC

region A (liquid)

• In region B, • — when the temperature drops to 58ºC, octadecan-1-ol begins to solidify • — both solid and liquid states exist • — the temperature remains constant though the temperature of the mixture is higher than the room temperature

region B (solid + liquid)

region C (solid)

Time/ minutes 288

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6.2 Cooling curve of a substance (SB p.174) Cooling curve of octadecan-1-ol

Temperature / ºC

region A (liquid)

• In region C, • —all the octadecan-1-ol has been solidified, and exists in solid state only • —its temperature drops again • —the temperature drops to room temperature, and solidification stops

region B (solid + liquid)

region C (solid)

Time/ minutes 289

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6.2 Cooling curve of a substance (SB p.174) Explanation of the cooling curve Temperature/ ºC

temperature drops

region A (liquid)

region C (solid)

Time/ minutes

•

In regions A and C,

•

—

• •

— —

the temperature of octadecan-1-ol is higher than the room temperature, energy flows to the surroundings, and so its energy decreases this energy is come from its molecular kinetic energy

since the temperature of a substance is proportional to its molecular kinetic energy, it temperature drops

290

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6.2 Cooling curve of a substance (SB p.175) Explanation of the cooling curve Temperature/ ºC

constant temperature region B (solid + liquid)

Time/ minutes

• In region B, energy still flows to the surroundings, but the temperature • — remains constant the released energy does not come from the molecular kinetic • — energy, but the intermolecular potential energy, called latent heat since the temperature is independent of the latent heat, it • — remains constant even when state changes

291

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6.2 Cooling curve of a substance (SB p.175) Explanation of the cooling curve

Latent heat when a solid melts at melting point, it absorbs latent heat of fusion

when a liquid solidifies at freezing point, it releases latent heat of fusion

• — Latent heat is the energy transferred during the change of state When a solid changes to a liquid, the energy absorbed by it is called the latent • — heat of fusion. Conversely, when a liquid changes to a solid, it releases the same amount of energy

292

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6.2 Cooling curve of a substance (SB p.175)

Class Practice 1:

Temperature/ ºC

•(a) A solid is heated by a heater of power 200 W until its temperature is higher than its melting point. From the given temperature-time graph of the solid, determine the melting point and calculate the latent heat of it.

Time/s

70ºC . •The melting point of the solid is 　　　　　　 The energy supplied by •The latent heat of the solid = the heater during the process of melting

•　　　　 •　　　　 •　　　　 293

= Power × Time 200 × (80 – 20) = ˍˍˍˍˍˍˍˍˍˍˍ Ans 12 000 J wer = ˍˍˍˍˍˍˍˍˍˍˍ Manhattan Press (H.K.) Ltd. © 2001

6.2 Cooling curve of a substance (SB p.176)

Class Practice 1 (Cont’d)

•(b) When the molecules of a substance absorb latent heat during a change of state, their molecular increase

separations _______________. •The absorbed energy is stored in the form of intermolecular potential energy _________________________________. Ans wer 294

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Section 6.3 Specific Latent Heat of Fusion • Measurement of specific latent heat of fusion of ice Manhattan Press (H.K.) Ltd. © 2001

6.3 Specific latent heat of fusion (SB p.176)

Specific latent heat of fusion • Specific latent heat of fusion (f) Heat required to change 1 kg of the substance from solid state to liquid state without temperature change • — Unit: J kg–1 E f = • — Expressed as the formula m • — Specific latent heat of fusion of ice is 3.34 × 105 J kg–1 •

—

296

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6.3 Specific latent heat of fusion (SB p.176)

Specific latent heat of fusion (f) for some common substances •Mercury •Oxygen •Lead •Sulphur •Alcohol •Copper •Ice •Aluminium 297

11 kJ kg–1 14 kJ kg–1 25 kJ kg–1 39 kJ kg–1 110 kJ kg–1 210 kJ kg–1 334 kJ kg–1 400 kJ kg–1

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Measurement of specific latent Experiment 6B heat of fusion of ice Specific latent heat of fusion of ice (f)

6.3 Specific latent heat of fusion (SB p.177)

Expt. VCD

f = ???

298

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6.3 Specific latent heat of fusion (SB p.177)

Measurement of specific latent heat of fusion of ice

Experiment 6B Experimental set — The heater is connected to the power supply

299

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6.3 Specific latent heat of fusion (SB p.177)

Experiment 6B

Measurement of specific latent heat of fusion of ice

Control set — The heater is not connected to the power supply — Find out the amount of ice melted by the surroundings (except the heater) — At room temperature, the ice will gain heat from the surroundings, so a control set is required

300

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6.3 Specific latent heat of fusion (SB p.177)

Measurement of specific latent heat of fusion of ice

Experiment 6B •The specific latent heat of fusion of ice can be calculated by: E f = m1 − m2 E : Energy supplied by heater to the crushed ice m1 : Mass of water and beaker in experimental set m2 : Mass of water and beaker in control set 301

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6.3 Specific latent heat of fusion (SB p.178)

Experiment 6B Precautions

Measurement of specific latent heat of fusion of ice

• 1. Melting ice is used (ice at 0ºC) to ensure no extra energy is needed to raise the temperature of the ice to 0ºC • 2. Crushed ice is used to enhance the thermal contact between the ice and the heater, so more heat from the heater is absorbed by the crushed ice

302

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Class Practice 2

6.3 Specific latent heat of fusion (SB p.179)

Measurement of specific latent heat of fusion of ice

When the temperature of 0.1 kg of water rises from 0 ºC to 50 ºC, the water absorbs ___________________________________ of energy. 0.1 × 4 200 × (50 – 0) = 21 000 J

When the same mass of ice at 0 ºC melts to water at 50 ºC, it absorbs of 0.1 × (3.34 ×___________________________________ 105) + 21 000 = 54 000 J energy. ice Ans a few pieces of ice coolant. Thus, Hence, __________________ is a better the

quick303way to cool a drink to(H.K.) drop Manhattanis Press Ltd. © 2001

wer

Section 6.4 Specific Latent Heat of Vaporization • Measurement of specific latent heat of vaporization of water • Evaporation and boiling Manhattan Press (H.K.) Ltd. © 2001

6.4 Specific latent heat of vaporization (SB p.180)

Latent heat of vaporization — Heat required to change a liquid to a gas without temperature change When a liquid vaporizes at the boiling point, it absorbs latent heat of vaporization

When a gas condenses at the condensation point, it releases latent heat of vaporization 305

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The potential energy of molecules increases

6.4 Specific latent heat of vaporization (SB p.180)

Specific latent heat of vaporization (v) • — Energy required to change 1 kg of a substance from liquid state to gaseous state without temperature change • — Expressed as the formula

E v = 　　 m

• — Specific latent heat of vaporization of water is 2.26 × 106 J kg–1

306

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6.4 Specific latent heat of vaporization (SB p.180)

Energy absorbed and released during the change of states of a substance absorbs latent heat of vaporization

absorbs latent heat of fusion

solid

307

releases latent heat of fusion

liquid

releases latent heat of vaporization

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gas

6.4 Specific latent heat of vaporization (SB p.182)

Experiment 6C Measurement of specific latent heat of vaporization of water Specific latent heat of vaporization of water Expt. VCD

308

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6.4 Specific latent heat of vaporization (SB p.182) Measurement of specific latent heat of vaporization of water

Experiment 6C

•The specific latent heat of vaporization of water can be E obtained by: v = m E : Energy supplied from the heater to the crushed ice m : Mass of vaporized water

309

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6.4 Specific latent heat of vaporization (SB p.182) Measurement of specific latent heat of vaporization of water

Experiment 6C Precautions

• 1. Due to the heat loss, the experimental value is higher than the accepted value of v • 2. Using a polystyrene cup instead of a beaker can improve the accuracy

310

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6.4 Specific latent heat of vaporization (SB p.185) • • •

Wet clothes dry up

• • •

311

Evaporation and boiling

Evaporation — Require specific latent heat of vaporization — Molecules near the liquid surface gain sufficient energy to escape from the surface, so evaporation occurs only at the surface of a liquid — Occurs at any temperature — The process speeds up in dry and windy days — The body temperature is regulated by the evaporation of sweat

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6.4 Specific latent heat of vaporization (SB p.185)

Evaporation and boiling

• Boiling require latent heat of • — vaporization occurs only at the boiling point • — occurs throughout the liquid • — with bubbles appeared

312

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Chapter 7 Kinetic Theory and Gas Laws 7.1 7.2 7.3 7.4

Matter Properties of Gas Gas Laws Simulations of Gas Laws by Kinetic Theory Model Manhattan Press (H.K.) Ltd. © 2001

Section 7.1 Matter • Kinetic theory • Energy involved in change of state Manhattan Press (H.K.) Ltd. © 2001

Kinetic theory

7.1 Matter (SB p.195)

Kinetic theory All matter is made up of very tiny particles, called • — atoms, molecules and ions The particles are fast-moving • — When they are forced too close together, they • — repel each other strongly When they are slightly apart, they attract each • — other When they are widely separated, the attractive • — forces between them are negligible The temperature of a body depends on the • — average kinetic energy of its particles 315

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Kinetic theory

7.1 Matter (SB p.196)

Three states of matter: solid, liquid and gas

solid

316

liquid

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gas

Kinetic theory

7.1 Matter (SB p.196)

Property of a solid What is the property of a solid? •

Rigid, and have definite shape • Why? Molecules are arranged in a regular pattern, closely packed and held by strong intermolecular forces 317

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Kinetic theory

7.1 Matter (SB p.196)

Heating a solid • Molecules of a solid • — Restricted, but not stationary • — Vibrate slightly • — When temperature rises, the vibration is much vigorous, and its kinetic energy increases 318

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Kinetic theory

7.1 Matter (SB p.196)

Property of a liquid Liquid has definite volume but no • — definite shape The attractive forces between the molecules are not strong enough to hold them in fixed positions

• —

The liquid molecules are so energetic that they are free to slip past one another

• —

319

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Kinetic theory

7.1 Matter (SB p.197)

Heating a liquid

•When a liquid is heated, its temperature increases but the expansion of its volume is limited

320

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Kinetic theory

7.1 Matter (SB p.197)

Property of a gas • — The attraction between molecules is

so weak that can be neglected, so it can occupy the whole container Gas molecules move rapidly and randomly

• — • —

A gas has no definite volume and

shape

321

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7.1 Matter (SB p.198)

Energy involved in change of state

Heating Heating acurve of a body: heating a Evaporation Heating Melting of a liquid a and solidboiling of a liquid gas solid •Temperature •Kinetic •energy

Temperature

•Potential •energy

melting point

Time

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•Internal •energy

Section 7.2 Properties of Gas • • •

Descriptions of gas Kinetic theory model Brownian motion Manhattan Press (H.K.) Ltd. © 2001

7.2 Properties of gas (SB p.199)

Description of gas

Volume of a gas is identical to the volume of the container holding it

gas molecules

324

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7.2 Properties of gas (SB p.199)

Description of gas

Temperature of a gas ∝ average kinetic energy of its molecules

50ºC

20ºC

325

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Description of gas

7.2 Properties of gas (SB p.200)

Origin of gas pressure Gas molecules hit the inner surface of the balloon gas pressure

gas pressure

molecule 326

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inner surface of the balloon

7.2 Properties of gas (SB p.199)

Description of gas

Class Practice 1: As shown in the figure, two containers A and B holding two different gases are at temperatures of 20 °C and 50 °C respectively. •The volume occupied by the gas A is

greater ˍˍˍˍˍˍ than that occupied by the gas in B. Besides, the average

container A kinetic energy of the molecules of gas at 20 °C in A is ˍˍˍˍˍˍthan that of the

container B at 50 °C

gas in B.

smaller Ans wer 327

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7.2 Properties of gas (SB p.200)

Description of gas

Pressure •Pressure of a gas is defined as: Force perpendicu lar to the surface Pressure = 　 Area of the surface F Or：　　P = A

•The unit of pressure is pascal (Pa) •1 Pa = 1 N m-2 328

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7.2 Properties of gas (SB p.200)

Description of gas

Normal atmospheric pressure •Normal atmospheric pressure is about 1.02 × 105 Pa •Therefore, on a 25 m2 floor, the force exerted is F=P× A • = (1.02 × 105) × 25 • = 2.55 × 106 N • 329

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Description of gas

7.2 Properties of gas (SB p.200)

Class Practice 2 •The tyre of a car is pumped to a pressure of 2 × 20 N

105 Pa. It means that a force of ________________ is exerted on every 1 cm2 of the inner F = Psurface × A = 2of×the 105tyre. × (1 × 10-4 ) = 20 N Ans wer 330

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7.2 Properties of gas (SB p.201)

Examples of gas pressure

331

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Description of gas

7.2 Properties of gas (SB p.202)

Experiment 7A model

Kinetic theory

Intro VCD

Expt. VCD

332

Kinetic theory model

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Kinetic theory model

7.2 Properties of gas (SB p.203)

Simulation of motion of gas by model piston piston

volume

vibrating vibrating platform platform voltage vibrator vibrator 333

•In this model,

— each ball bearing represents a gas molecule ball bearing — the applied voltage represents the temperature of the gas — the weight of the piston represents the pressure of the gas — the volume of the enclosed tube represents the volume occupied by the gas

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Kinetic theory model

7.2 Properties of gas (SB p.203)

Temperature rises, volume increases Gas expands Gas pressure increases Gas molecules collide the wall of the tube more violently and frequently

↑voltage

Energy of gas molecules increases, speed of motion increases Temperature rises

334

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7.2 Properties of gas (SB p.203)

Kinetic theory model

Class Practice 3

•In the kinetic theory model, the pressure exerted by the ball voltage bearings can be increased by increasing the ˍˍˍˍˍˍˍ more ball bearings and adding into the tube.

Ans wer 335

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7.2 Properties of gas (SB p.204)

Brownian motion

How do pollen grains move in the water?

pollen grains

336

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Brownian motion Brownian motion : Pollen grains bombard with water molecules to give rise to an irregular motion

7.2 Properties of gas (SB p.204)

water molecule

pollen grains

337

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Section 7.3 Gas Laws • Pressure and volume relationship (constant temperature) • Pressure and temperature relationship (constant volume) • Volume and temperature relationship (constant pressure) Manhattan Press (H.K.) Ltd. © 2001

7.3 Gas laws (SB p.205)

Measuring gas pressure curved metal tube

gas pressure

Bourdon gauge 339

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pointer

7.3 Gas laws (SB p.205)

T, V and P are interrelated temperature

pressure

volume

340

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7.3 Gas laws (SB p.205)

Pressure and volume relationship (constant temperature)

Experiment 7B Pressure-volume relationship of air

•The rubber tubing should be short, use oil to grease the junction •The air pump should be pushed slowly to prevent any increase in Expt. VCD temperature 341

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Experiment 7B Graph showing the relationship between P and V

7.3 Gas laws (SB p.206)

342

Pressure and volume relationship (constant temperature)

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Experiment 7B Graph showing the relationship between P 1 V and

7.3 Gas laws (SB p.206)

343

Pressure and volume relationship (constant temperature)

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Pressure and volume relationship (constant temperature)

7.3 Gas laws (SB p.207)

Boyle’s law •Boyle’s law states that for a fixed mass of gas, its pressure is inversely proportional to its volume, provided the gas temperature remains constant P1 V2 = 　or　P1V1 = P2V2 P2 V1

344

PV = constant

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Pressure and volume relationship (constant temperature)

7.3 Gas laws (SB p.207)

An alternative method to study Boyle’s law

 Wait for steady readings  Slowly pull out the piston syringe

rubber tubing

piston

 Make the  Grease the junction with oil rubber tube

as short as possible

345

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Bourdon gauge

Pressure and volume relationship (constant temperature)

7.3 Gas laws (SB p.208)

Class Practice 4: The pressure and the volume of the air column in the Boyle’s law apparatus are recorded in the following table. Complete the table. Pressure (P) / kPa

100

64.4

120

53.7

140

46.0

160

40.3

180

35.8

200 346

Volume (V) / cm3

32.2 Manhattan Press (H.K.) Ltd. © 2001

Ans wer

7.3 Gas laws (SB p.205)

Pressure and volume relationship (constant temperature)

Explanation of Boyle’s law by the kinetic theory of gas •Assume a gas is compressed at a constant temperature, ∀→the distances between the gas molecules and the container wall decrease ∀→the gas molecules collide with the container wall more frequently P V ∀→ the gas pressure increases 347

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7.3 Gas laws (SB p.209)

Pressure and temperature relationship (constant volume)

Experiment 7C Pressure-temperature relationship of air • The thermometer and the flask should not touch the bottom of the beaker • The whole flask must be immersed in water

•All the junction must be greased with oil

Expt. VCD 348

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7.3 Gas laws (SB p.210)

Pressure and temperature relationship (constant volume)

Experiment 7C Relationship between pressure and Celsius temperature

349

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7.3 Gas laws (SB p.211)

Class Practice 5

Ans wer

•A typical P-T graph is shown in the figure above. If another identical flask containing the same gas of a greater mass is used, sketch the new P-T relationship on the figure. Explain the shape of the graph. The pressure of a gas depends also on its mass. The

larger the mass of a gas, the larger will be the number of gas molecules hitting the container wall per second. A higher pressure is resulted. However, the temperature for zero pressure should be the same for all gases. 350

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Pressure and temperature relationship (constant volume)

7.3 Gas laws (SB p.211)

Absolute temperature •Absolute temperature •＝ Celsius temperature + 273 0 K is the absolute zero temperature

•

•e.g. •the boiling point of water is 100ºC, i.e.373K •the freezing point of water is 0ºC, i.e. 273K 351

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Pressure and temperature relationship (constant volume)

7.3 Gas laws (SB p.211)

Class Practice 6 Complete the following table for the unknown temperature of a gas. Celsius Celsius temperature // ° C ° temperature C Absolute Absolute temperature // K K temperature

20

45

57

80 107 135 135

293 318 330 353 380 380 408

Ans wer 352

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7.3 Gas laws (SB p.212)

Pressure and temperature relationship (constant volume)

Relationship between pressure and absolute temperature Ｐ T (V is constant)

353

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Pressure and temperature relationship (constant volume)

7.3 Gas laws (SB p.212)

Pressure law •Pressure law states that for a fixed mass of gas, its pressure is directly proportional to its absolute temperature, provided the volume of the gas remains constant

P1 P2 = T1 T2

P 　　　 = constant T

•Note: T is the absolute temperature 　 354

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Pressure and temperature relationship (constant volume)

7.3 Gas laws (SB p.212)

Pressure law •Volume is unchanged •（ V is constant ） T1

T1

P1

355

P1 P2 　= T1 T2

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P2

Pressure and temperature relationship (constant volume)

7.3 Gas laws (SB p.213)

Class Practice 7 •A container holds a gas at 27ºC . To what temperature must it be heated for its pressure to double in value? Assume that the volume of the gas is fixed. From

From

We obtain: We obtain: or

356

or

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Ans wer

7.3 Gas laws (SB p.213)

Pressure and temperature relationship (constant volume)

Explanation of pressure law by the kinetic theory of gas

• A gas is heated at a constant volume ∀ → The speed of the gas molecules increases ∀ → The gas molecules collide with the container wall more violently and frequently P T ∀ → The gas pressure increases 357

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7.3 Gas laws (SB p.214)

Volume and temperature relationship (constant pressure)

Experiment 7D Volume-temperature relationship of air Expt. VCD

358

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Volume and temperature relationship (constant pressure)

7.3 Gas laws (SB p.214)

Experiment 7D Precautions thermometer

air column

359

capillary tube ruler stirrer

ice-water mixture mercury thread

• Stir the water bath thoroughly • Keep one end of the capillary tube open to let the pressure of the air pressure constant

•Immerse the whole air column in water •A thin capillary tube is used

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7.3 Gas laws (SB p.215)

Volume and temperature relationship (constant pressure)

Relationship between volume and absolute temperature

V∝T (P is constant)

360

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7.3 Gas laws (SB p.217)

Volume and temperature relationship (constant pressure)

Charles’ law •Charles’ law states that for a fixed mass of gas, its volume is directly proportional to its absolute temperature, provided the pressure of the gas remains constant V1 V2 V = 　　 = constant T T1 T2 •Note: T is the absolute temperature 　　 361

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7.3 Gas laws (SB p.218)

Volume and temperature relationship (constant pressure)

Explanation of Charles’ law by the kinetic theory of gas

• ∀ ∀ ∀

A gas is heated at a constant pressure → The speed of gas molecules increases → Its molecules hit the container wall more frequently and violently → In order to keep the pressure constant, the volume must be increased

T 362

V Manhattan Press (H.K.) Ltd. © 2001

General gas law

7.3 Gas laws (SB p.218)

General gas law Ｔ

1

Ｔ

V1

V2

P1

P2

P1 V1 P2 V2 = T1 T2 363

2

PV = constant T

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Section 7.4 Simulations of Gas Laws by Kinetic Theory Model • Simulation of Boyle’s law • Simulation of Pressure law • Simulation of Charles’ law • Simulation of Brownian Manhattan Press (H.K.) Ltd. © 2001

7.4 Simulations of gas laws by kinetic theory model (SB p.219)

Simulation of motions of gas molecules piston

volume

365

gas pressure (P)

gas volume (V)

ball bearing

gas molecule

vibrator

temperature of gas (T )

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7.4 Simulations of gas laws by kinetic theory model (SB p.219) Simulation of Boyle’s law

Simulation of Boyle’s law pressure (P)↑ volume (V)↓ temperature (T) remains unchanged

366

add weights

weights of piston

reduces

volume

voltage of vibrator

remains unchanged

Manhattan Press (H.K.) Ltd. © 2001

weight

7.4 Simulations of gas laws by kinetic theory model (SB p.219) Simulation of Pressure law

Simulation of Pressure law pressure (P)↑

increases

weights of piston

volume (V) remains unchanged

volume

temperature (T)↑

voltage of vibrator

367

remains unchanged

increases

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weight

7.4 Simulations of gas laws by kinetic theory model (SB p.220) Simulation of Charles’ law

Simulation of Charles’ law pressure (P) remains unchanged

volume (V)↑

temperature (T )↑

weights of piston

remains unchanged

ball bearing

volume

increases vibrating platform

voltage of vibrator increases

vibrator 368

piston

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7.4 Simulations of gas laws by kinetic theory model (SB p.221) Simulation of Brownian motion

Simulation of Brownian motion piston

ball bearing

ball bearing sphere

vibrating platform

sphere

vibrator 369

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7.4 Simulations of gas laws by kinetic theory model (SB p.221) Difference between real gas and gas model

During collisions kinetic theory model

loss of energy -replenished by the vibrating platform

motion of gas molecules

370

no energy loss

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The End

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