Summary 21
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Physics/D'Amato 2007 Unit 21
Page 43
Period ____ Name _________________________________
Unit 21 Summary of definitions and relationships 1. A light ray is an imaginary arrow which shows the direction light travels. A beam of light is real, like a laser, containing many light rays that are mostly going in the same direction.
(Illustrate with your own picture)
2. Objects like a candle flame, light bulb, and the sun are luminous objects which create light and send rays in every direction from every point on the object.
(Illustrate with your own picture)
3. Light rays reflect in all directions from the surfaces of normal objects. An illuminated object is reflecting light rays. If an object is visible to you, a light ray from the object is entering your eye.
(Illustrate with your own picture)
4. We create ray diagrams to reason about the interaction of light and objects. Draw enough rays to tell the story. Remember, light rays go in every direction from every point on a luminous or illuminated object. This ray diagram shows that there is an area of dark shadow directly behind the block where no light rays fall and the rest of the wall is illuminated.
5. Any two lines can be described in terms of the angle between them. The lines may be real or imaginary or both, but there are always two lines. Measure from the point where the lines come together. We often use the greek letter θ (theta) to stand for an unknown angle.
Chris D'Amato PTHS 2007. Portions copyright (c) 2006 A. Van Heuvelen and E. Etkina
Light bulb
Block
Wall
An angle is between two lines 0° 30°
90°
Physics/D'Amato 2007 Unit 21
Page 44
Period ____ Name _________________________________
6. Many topics in the study of light depend on the concept of a normal line. The normal line is an imaginary line that is perpendicular to the surface at the point of reflection or refraction. r A normal line can be labelled with N for clarity.
Normal r line N
90°
Surface
7. On a curved surface, the normal is perpendicular to the tangent. On a circle or section of a circle, the normal always runs through the center of the circle.
8. The law of reflection: a light beam is incident to a smooth reflecting surface at some incident angle θ1 to the normal line. The beam reflects off the other side of the normal line at the same angle θ 2 from the normal line. Angles are always measured between the light ray and the normal line.
9. If a surface is smooth at the microscopic level, like a mirror, the normal lines at different locations are parallel to each other. Thus, parallel incident rays are reflected at the same angle. This type of reflection is called specular reflection.
Normal line
90°
Normal line Incident ray
θ1 θ 2 Reflected ray Mirror
Incident rays
Mirror
10. Ordinary surfaces are rough and bumpy at the microscopic level, and the normal lines point in all different directions. Thus, parallel incident rays will be reflected in all directions. A beam of light will be reflected diffusely in all directions, so this is called diffuse reflection.
Incident rays
Ordinary surface
Chris D'Amato PTHS 2007. Portions copyright (c) 2006 A. Van Heuvelen and E. Etkina
Physics/D'Amato 2007 Unit 21
Page 45
11. When light travels from one medium into another medium (like going from air into water) its path changes when it crosses the surface. This is called refraction. A normal line is imagined, perpendicular to the surface between the two media, at the point the light ray crosses. Going from air into something else, the ray crosses the normal line and bends towards the normal in the other medium. Going from something else into air, the ray crosses the normal line again and bends away from the normal.
12. Different substances cause light to refract by different amounts. The amount of refraction is a characteristic of the substance, and this is called the substance's index of refraction n. It is a number equal to or greater than 1 which represents how much the light bends relative to air.
13. Snell's law relates the incident angle and the refracted angle of a beam of light as it passes from one material to another. The incident angle θ1 (in the incident medium) and the refracted angle θ1 (in the refractive medium) are measured from the normal. We use subscripts like 1 and 2 to indicate different values of a variable – like θ1 and θ 2 which indicate two different angles. Subscripts must be used carefully but we don't do any math with the subscript numbers themselves!
14. The four terms of Snell's law can be rearranged like any other algebraic expression to isolate any variable.
Period ____ Name _________________________________
air
something else air
Some common index of refraction values: air n =1 water n = 1.33 glass
n ≈ 1.5
Snell's law: n1 sin θ1 = n2 sin θ 2
incident medium refractice index n1
θ1
refractive medium refractive index n2
θ2
n1 sin θ1 = n2 sin θ 2 n1 =
n2 sin θ 2 sin θ1 ⎛ n1 sin θ1 ⎞ ⎟ ⎝ n2 ⎠
θ 2 = sin −1 ⎜
Chris D'Amato PTHS 2007. Portions copyright (c) 2006 A. Van Heuvelen and E. Etkina
Physics/D'Amato 2007 Unit 21
Page 46
15. Sine (abbreviated sin) is a function that takes any angle θ from 0° to 360° and returns the height of a right triangle drawn in the unit circle as shown. Your calculator knows the value of sine for any angle, but you need to know what it means. The function arcsin(x) or sin-1(x) is the inverse sine and it means "the angle that has a sine of x"
Period ____ Name _________________________________
(0,1)
90°
(cos θ ,sin θ )
1
sin θ
θ (0, 0)
16. When light moving in a medium of higher refractive index (for example, glass or water) is incident on the interface with a medium of smaller refractive index (for example, air), the refracted ray bends away from the normal line. When the incident angle reaches a so-called critical angle θc, the refracted angle is 900. At incident angles greater than θc, there is no refracted light. All of the light is reflected – called total internal reflection.
0° (1, 0)
cos θ
n2 < n1 surface
n1
θC n2 < n1 surface
n1
θ > θC
Chris D'Amato PTHS 2007. Portions copyright (c) 2006 A. Van Heuvelen and E. Etkina
90°
Page 43
Period ____ Name _________________________________
Unit 21 Summary of definitions and relationships 1. A light ray is an imaginary arrow which shows the direction light travels. A beam of light is real, like a laser, containing many light rays that are mostly going in the same direction.
(Illustrate with your own picture)
2. Objects like a candle flame, light bulb, and the sun are luminous objects which create light and send rays in every direction from every point on the object.
(Illustrate with your own picture)
3. Light rays reflect in all directions from the surfaces of normal objects. An illuminated object is reflecting light rays. If an object is visible to you, a light ray from the object is entering your eye.
(Illustrate with your own picture)
4. We create ray diagrams to reason about the interaction of light and objects. Draw enough rays to tell the story. Remember, light rays go in every direction from every point on a luminous or illuminated object. This ray diagram shows that there is an area of dark shadow directly behind the block where no light rays fall and the rest of the wall is illuminated.
5. Any two lines can be described in terms of the angle between them. The lines may be real or imaginary or both, but there are always two lines. Measure from the point where the lines come together. We often use the greek letter θ (theta) to stand for an unknown angle.
Chris D'Amato PTHS 2007. Portions copyright (c) 2006 A. Van Heuvelen and E. Etkina
Light bulb
Block
Wall
An angle is between two lines 0° 30°
90°
Physics/D'Amato 2007 Unit 21
Page 44
Period ____ Name _________________________________
6. Many topics in the study of light depend on the concept of a normal line. The normal line is an imaginary line that is perpendicular to the surface at the point of reflection or refraction. r A normal line can be labelled with N for clarity.
Normal r line N
90°
Surface
7. On a curved surface, the normal is perpendicular to the tangent. On a circle or section of a circle, the normal always runs through the center of the circle.
8. The law of reflection: a light beam is incident to a smooth reflecting surface at some incident angle θ1 to the normal line. The beam reflects off the other side of the normal line at the same angle θ 2 from the normal line. Angles are always measured between the light ray and the normal line.
9. If a surface is smooth at the microscopic level, like a mirror, the normal lines at different locations are parallel to each other. Thus, parallel incident rays are reflected at the same angle. This type of reflection is called specular reflection.
Normal line
90°
Normal line Incident ray
θ1 θ 2 Reflected ray Mirror
Incident rays
Mirror
10. Ordinary surfaces are rough and bumpy at the microscopic level, and the normal lines point in all different directions. Thus, parallel incident rays will be reflected in all directions. A beam of light will be reflected diffusely in all directions, so this is called diffuse reflection.
Incident rays
Ordinary surface
Chris D'Amato PTHS 2007. Portions copyright (c) 2006 A. Van Heuvelen and E. Etkina
Physics/D'Amato 2007 Unit 21
Page 45
11. When light travels from one medium into another medium (like going from air into water) its path changes when it crosses the surface. This is called refraction. A normal line is imagined, perpendicular to the surface between the two media, at the point the light ray crosses. Going from air into something else, the ray crosses the normal line and bends towards the normal in the other medium. Going from something else into air, the ray crosses the normal line again and bends away from the normal.
12. Different substances cause light to refract by different amounts. The amount of refraction is a characteristic of the substance, and this is called the substance's index of refraction n. It is a number equal to or greater than 1 which represents how much the light bends relative to air.
13. Snell's law relates the incident angle and the refracted angle of a beam of light as it passes from one material to another. The incident angle θ1 (in the incident medium) and the refracted angle θ1 (in the refractive medium) are measured from the normal. We use subscripts like 1 and 2 to indicate different values of a variable – like θ1 and θ 2 which indicate two different angles. Subscripts must be used carefully but we don't do any math with the subscript numbers themselves!
14. The four terms of Snell's law can be rearranged like any other algebraic expression to isolate any variable.
Period ____ Name _________________________________
air
something else air
Some common index of refraction values: air n =1 water n = 1.33 glass
n ≈ 1.5
Snell's law: n1 sin θ1 = n2 sin θ 2
incident medium refractice index n1
θ1
refractive medium refractive index n2
θ2
n1 sin θ1 = n2 sin θ 2 n1 =
n2 sin θ 2 sin θ1 ⎛ n1 sin θ1 ⎞ ⎟ ⎝ n2 ⎠
θ 2 = sin −1 ⎜
Chris D'Amato PTHS 2007. Portions copyright (c) 2006 A. Van Heuvelen and E. Etkina
Physics/D'Amato 2007 Unit 21
Page 46
15. Sine (abbreviated sin) is a function that takes any angle θ from 0° to 360° and returns the height of a right triangle drawn in the unit circle as shown. Your calculator knows the value of sine for any angle, but you need to know what it means. The function arcsin(x) or sin-1(x) is the inverse sine and it means "the angle that has a sine of x"
Period ____ Name _________________________________
(0,1)
90°
(cos θ ,sin θ )
1
sin θ
θ (0, 0)
16. When light moving in a medium of higher refractive index (for example, glass or water) is incident on the interface with a medium of smaller refractive index (for example, air), the refracted ray bends away from the normal line. When the incident angle reaches a so-called critical angle θc, the refracted angle is 900. At incident angles greater than θc, there is no refracted light. All of the light is reflected – called total internal reflection.
0° (1, 0)
cos θ
n2 < n1 surface
n1
θC n2 < n1 surface
n1
θ > θC
Chris D'Amato PTHS 2007. Portions copyright (c) 2006 A. Van Heuvelen and E. Etkina
90°
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