JEE Main · 2004 · 24 Apr 2004 · Offline · Geometrical Optics

A light ray is incident perpendicular to one face of a

9 0^{\circ}

prism and is totally internally reflected at the glass-air interface. If the angle of reflection is

4 5^{\circ}

, we conclude that the refractive index

n

(A) $n < \frac{1}{2}$
(B) $n > 2$ ✓ Correct
(C) $n > \frac{1}{2}$
(D) $n < 2$

Answer: (B)

Solution

The ray enters normally through one face and runs on undeviated until it meets the hypotenuse at

4 5^{\circ}

. For it to be totally reflected there,

4 5^{\circ}

must exceed the critical angle

C

, where

sin C = \frac{1}{n}

. Thus

sin 4 5^{\circ} > \frac{1}{n}

, that is

\frac{1}{2} > \frac{1}{n}

, which means the refractive index must be greater than

2

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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