question_answer

A rod of glass (m = 1.5) and of square cross section is bent into the shape shown in the figure. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of circular arc then for what maximum value of \[\frac{d}{R}\] light entering the glass slab through surface A emerges from the glass through B

A)            1.5

B)            0.5

C)            1.3

D)            None of these

Correct Answer: B

Solution :

                   Consider the figure if smallest angle of incidence q is greater than critical angle then all light will emerge out of B Þ \[\theta \ge {{\sin }^{-1}}\left( \frac{1}{\mu } \right)\Rightarrow \sin \theta \ge \frac{1}{\mu }\] from figure \[\sin \theta =\frac{R}{R+d}\] Þ \[\frac{R}{R+d}\ge \frac{1}{\mu }\Rightarrow \left( 1+\frac{d}{R} \right)\le \mu \] Þ \[\frac{d}{R}\le \mu -1\Rightarrow {{\left( \frac{d}{R} \right)}_{\max }}=0.5\]