question_answer

A light ray falls on square glass slab as shown in the diagram. The index of refraction of the glass, if total internal reflection is to occur at the vertical face, is equal to:    [JEE ONLINE 23-04-2013]

A)             \[\left( \sqrt{2}+1 \right)/2\]

B) \[\sqrt{\frac{3}{2}}\]

C)              \[\frac{3}{2}\]           

D) \[\sqrt{\frac{3}{2}}\]

Correct Answer: D

Solution :

[d] At point A by Snell’ slaw

(i)

At point B, for total internal reflection,

From figure,

(ii)

Now

From eqs (ii) and (iii)

Squaring both sides and then solving, we get