question_answer

A ray of light travels from a medium of refractive index n into air. If the angle of incidence at the plane surface of separation is \[\theta \] and the corresponding angle of deviation is \[\delta ,\] the variation of \[\delta \] with \[\theta \] is shown correctly in the figure

A)          

B)          

C)            

D)

Correct Answer: A

Solution :

Using Snell's law at the interface,

\[n\sin \theta =1\operatorname{sino}|\]

or \[o|=si{{n}^{-1}}(nsin\theta )\]

Deviation,\[\delta =o|-\theta \]     ...(i)

or \[\delta ={{\sin }^{-1}}(nsin\theta )-\theta \]     ...(ii)

This is a non-linear relation. Therefore, choice is between (A) and (C).

When \[\theta ={{\theta }_{c}},\,o|=\pi /2\,\]

\[\therefore \]Maximum value of \[\delta \]from (i) is

\[{{\delta }_{1}}=\frac{\pi }{2}-{{\theta }_{C}}\]

When \[\theta >{{\theta }_{C}}.\] total internal reflection occurs, and deviation \[\delta =\pi -2\theta \] i.e. \[\delta \]decreases linearly with \[\theta \]

\[{{\delta }_{2}}={{\delta }_{\max }}=\pi -2\,{{\theta }_{C}}=2{{\delta }_{1}}\]

Hence choice (A) is correct