Ray Optics

Objectives

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• The ray aspect of light. • The phenomenon of reflection and refraction of light. • The determination of speed of light. • The concepts related to mirrors, lenses, prisms etc. • The different phenomena like dispersion and scattering of light

Summary

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„ A ray of light gives the direction of light. „ Law of reflection is, i = r „ Paraxial rays are the rays travelling close to the principal axis of the mirror and make „ small angles with it. „ The relation between focal length and radius of curvature in spherical mirror is, 2 2 f R R = = (or) f „ Cartesian sign conventions are to be followed to trace image formed by spherical mirrors. „ The mirror equation is, 1 1 1 v u f + = „ The magnification in spherical mirror is, m h h v u = ′ = − , m h h f v f f f u = ′ = − = − „ Light travels with lesser velocity in optically denser medium. „ Refractive index is the ratio of speed of light in vacuum to speed of light in medium, n c = v „ Optical path is the equivalent path travelled in vacuum in the same time light travels through a optically denser medium. d n ′ = d „ Law of refraction also called as Snell’s law in ratio form is, sin sin i r n n = 2 1 . „ In product form is, n i n r 1 2 sin s = in „ The relative refractive index of second medium with respect to first medium is, n n n 21 2 1 = „ The apparent depth is always lesser than actual depth. The equation for apparent depth is, d′ = d n „ The critical angle of incidence i c for a ray incident from a denser to rarer medium, is that angle for which the angle of refraction is 90°. For i > i c , total internal reflection occurs. „ Equations for critical angle incidence is, sini n c = 1 (or) i n c =           − sin 1 1 „ Snell’s window is the restricted area of circular illumination which appears when seen from water due to critical angle incidence. The radius of the circular illumination is, R d n R d n = −            = − 1 1 1 2 2 ( ) or „ Optical fibre makes use of critical angle incidence. The acceptance angle in optical fibre is, . Here, n1 , n2 , n3 are the refractive indices of core, cladding and surrounding medium respectively. „ Glass slabs produce a lateral displacement on the light falling on it. The equation for lateral shift is, L t i r r = ( ) − ( )         „ The equation for single spherical surface is, n v u n R − =1 ( ) −1 „ The focal length of the thin lens is positive for a converging lens and negative for a diverging lens. It is not based on the position of the focal point. „ The lens makers formula is, 1 1 1 1 1 2 f n R R = − ( ) −            „ The lens equation is, 111 vuf - = „ The magnification produced by the lens is, m h h v u = =’ , m h h f f u = = + ’ (or) m h h f v f = =’ − „ The power of a lens is a measure of the degree of convergence (or) divergence of light falling on it. Power and focal length are inverse to each other. P f = 1 „ The unit of power is diopter (D) when the focal length is taken in meter. „ The effective focal length of lenses in contact is, 1 1 1 1 2 F f f = + „ A prism produces deviation on the incident ray. „ Angle of deviation depends on angle of prism, angle of incidence and refractive index of material of prism given by the equation, d i = +1 2i A − „ At minimum deviation, i 1 = i 2 , r1 = r2 , and the ray inside the prism is parallel to the base of the prism. „ The refractive index of prism depends on angle of prism and angle of minimum deviation given by the equation, n A D A =  +                    sin sin 2 2 „ When white light travels through a medium, different colours travel with different speeds leading to dispersion of light. Red colour travels faster than violet colour in a medium. In vacuum all the colours travel with the same speed. „ The angle of deviation produced by the small angled prism is, d = − ( ) n A 1 „ The angular separation between the two extreme colours (violet and red) in the spectrum is called angular dispersion. δV– δR = (nV–nR)A „ Dispersive power is the measure of ability of the medium to disperse white light. w = ( ) − − n n n V R ( )1 „ Rainbow is formed by dispersion of light by droplets of water. „ The scattering of light by particles of size less than wavelength of light is called Rayleigh scattering. The intensity of light produced by Rayleigh scattering is, I µ 1 4 l „ Non-Rayleigh scattering is by suspended dust particles whose size is greater than the wavelength of light. This scattering is independent of wavelength of light.