Examville.com - Refraction

REFRACTION 1. The bending of light when it passes obliquely from one transparent medium to another is called refraction.

(a). No refraction takes place if the ray of light enters from one medium to another at normal. (b). In going from a rarer to a denser medium, a ray of light bends towards the normal and in going from a denser to a rarer medium, a ray of light bends away from the normal. (c). The cause of refraction is that the speed of light is different in different media. The speed of light is less in an optically denser medium (e.g. glass) as compared to that in an optically rarer medium (e.g. air). (d). The frequency of refracted ray is the same as that of incident ray, It means that during refraction, speed as well as wavelength of light changes.

2. Law of refraction states that the sine of angle of incidence to the sine of angle of refraction is constant for two media. So, with reference to Fig. 1, we have, Sin i / sin r = constant = aμb

(Snell’s Law)

The constant aμb is called refractive index of medium B (in which the refracted ray travels) with respect to medium A (in which the incident ray travels). (a).Absolute refractive index of a medium can be defined in the following two ways: (i). Absolute refractive index, μ = sin i /sin r (incident ray in vacuum / air) (ii). Absolute refractive index μ = [velocity of light in vacuum / air (c)] / [velocity of light in the medium (v)] (b). The absolute refractive index of vacuum / air is 1. The refractive index is always positive. (c). The greater the refractive index of a medium, the smaller is the velocity of light in it or vice versa. 3. Snell’s law can also be written as, μ1sini = μ2 sin r Or,

μ sin i = constant

Where, μ1 is the absolute refractive index of the medium in which the incident ray travels, and μ2 is the absolute refractive index of the medium in which the refracted ray travels. 4. The refractive index of the denser medium with respect to rarer medium is equal to the reciprocal of the refractive index of rarer medium with respect to denser medium i.e. aμb

= 1 / (bμa)

If a μ b is refractive index of medium b with respect to air and a μ c is the refractive index of medium c with respect to air, then the refractive index of medium c with respect to medium b is bμc

= ( aμc) / (aμb)

5. An object placed in a denser medium (for e.g. water), when viewed from a rarer medium (e.g. air) appears to be at a lesser depth than its real depth. aμ

w=

real depth / apparent depth

Or we can say that aμb = real depth / apparent depth Where aμb is the refractive index of the denser medium b with respect to rarer medium a. Apparent depth = d = t [1 – 1 / (aμb)] Where t is the real depth.

6. When a ray of light passes from a denser medium to a rarer medium, it bends away from the normal. The angle of incidence in the denser medium for which the angle of refraction is 900 is known as critical angle C. If the pair of media is water – air, then aμ w

= 1 / sinC

Or we can say that aμb = 1 / sinC Where aμb is the refractive index of the denser medium b with respect to rarer medium a. 7. The conditions for total internal reflection are: (a). The light should travel from denser to a rarer medium. (b). The angle of incidence in the denser medium should be greater than the critical angle. Under the conditions of total internal reflection, the surface separation the denser medium and the rarer medium act as perfect mirror. 8. A refracting surface which forms a part of a sphere of transparent refracting material is called a spherical refracting surface, there are two types of spherical refracting surfaces i.e. concave spherical refracting surface and convex spherical refracting surface. 9. In dealing with refraction at spherical refracting surfaces, we use the same sign conventions as for spherical mirrors.

10. The formula for the refraction at spherical refracting surfaces (concave or convex), when light travels from a rarer medium (absolute refracting index μ1) to a denser medium (absolute refractive index μ2) is - (μ1 / u) + (μ2 / v) = (μ2 – μ1) / R Where v and u are the distance of image and object respectively from the pole of the spherical refracting surface and R is the radius of curvature of the spherical refracting surface. When light travels from a denser medium to rarer medium, there is only interchange of μ1 and μ2 in the above formula. - (μ2 / u) + (μ1 / v) = (μ1 – μ2) / R or, - { (- μ1 / v) + (μ2 / u) } = -(μ2 – μ1) / R or, (-μ1 / v) + (μ2 / u) = (μ2 – μ1) / R 11. A lens is any transparent object having two spherical; (generally) refracting surfaces. So, a ray of light suffers two refractions on passing through the lens. 12. Lenses are generally made up of glass and are of two types, (a) Concave lens or diverging lens (b) Convex lens or converging lens

13. Few general properties of both concave as well as convex lens are as follows: (a). If the lens is thin and the radii of curvature of the two refracting surfaces are equal, then geometrical centre of the lens is the optical centre (C). (b). When rays of light are incident on a lens in a direction parallel to the principal axis, the rays after refraction through the lens converge to ( in case of convex lens), or diverge from ( in case of concave lens), principal focus F on the principal axis.

(c). Since it does not matter whether the beam of light is incident from the left or the right, a lens has two symmetrical focal points, one on each side of the lens. (d). The distance between the focus (F) and the optical centre (C) of the lens is called focal length (f) of the lens. 14. The lens maker’s formula for both concave as well as convex lenses is 1 / f = (μ – 1)[(1 / R1) – (1 / R2)] Where R1 and R2 are the radii of curvature of the two surfaces of the lens and μ is the refractive index of the material of the lens with respect to surroundings. 15. The relation between v, u and f for concave as well as convex lens is 1 / f= (1 / v) – (1 / u) (a). The focal length of concave lens is negative and that of convex lens is positive. (b). Increasing the refractive index of lens material shortens its focal length, also the thicker the lens, the shorter is its focal length. 16. Linear magnification m produced by a lens is Linear magnification = m = (height of image) / (height of object) = h2 / h1 The linear magnification of a lens can be expressed in terms of image distance (v) and object distance (u). Linear magnification = m = v / u If m is positive, the imager is erect with respect to object. If m is negative. The image is inverted with respect to object.

17. The power of a lens is a measure of its ability to produce deviation (divergence or convergence) of light. A lens of large focal length produces less deviation of light than that of lens of short focal length. Power of lens, P = 1 / f (in meters) dioptre 18. When two lenses of focal length f1 and f2 are in contact with each other, the combination behaves as a single lens of focal length F given by 1 / F = 1 / f1 + 1 / f2 If P is the power of combination and P1 and P2 are the powers of individual lenses, then P = P1 + P2 19. If the image of a real object formed by a lens (concave or convex) is on the other side of the object then the image is real and inverted with respect to object. If the image is formed on the same side as the object, then the image is virtual and erect with respect to object. 20. A real image can be obtained on a screen while a virtual image cannot be obtained on the screen, however our eye can see the virtual image. ***************************************************