question_answer

For the given incident ray as shown in figure, the condition of total internal reflection of the ray will be satisfied if the refractive index of block will be:                                                                              [AIPMT 2002]

A)  \[\frac{\sqrt{3}+1}{2}\]

B)                   \[\frac{\sqrt{2}+1}{2}\]                                    

C)  \[\sqrt{\frac{3}{2}}\]    

D)                           \[\sqrt{\frac{7}{6}}\]

Correct Answer: C

Solution :

Key Idea: For total internal reflection angle of incidence should be greater than critical angle.

For total internal reflection to take place, angle of incidence > critical angle

i.e.,

or

or

but

and from figure,

So,

i.e.,                                         (i)

From Snell's law,

Thus Eq. (i) becomes

or

or