question_answer

A ray of light travels from a medium of refractive index m to air. Its angle of incidence in the medium is i, measured from the normal to the boundary, and its angle of deviation is d. d is plotted against i which of the following best represents the resulting curve

A)                                

B)                       

C)                                  

D)

Correct Answer: A

Solution :

                   The ray of light is refracted at the plane surface. However, since the ray is travelling from a denser to a rarer medium, for an angle of incidence (i) greater then the critical angle  the ray will be totally internally reflected.   For i < c; deviation d = r ? i with \[\frac{1}{\mu }=\frac{\sin i}{\sin r}\] Hence \[\delta ={{\sin }^{-1}}\left( \mu \sin i \right)-i\] This is a non-linear relation. The maximum value of d is \[{{\delta }_{1}}=\frac{\pi }{2}-c\]; where i = c and \[\mu =\frac{1}{\sin c}\] For i > c, deviation d  = p ? 2i d decreases linearly with i d2 = p ? 2 c = 2d1