A rectangular glass slab A B C D of refractive index n₁ is immersed in water of refractive index n₂ (n₁ n₂ ) . A ray of light is incident at the surface A B of the slab as shown. The maximum value of the angle of incidence _ such that the ray comes out only from the another surface C D is given by

Step-by-step solution

Rays comes out only from C D , means rays after refraction from A B get totally internally reflected at A D . From the figure, aligned r₁+r₂ & =90 r₁ & =90-r₂ (r₁ )_ & =90^ - (r₂ )_ and (r₂ )_ = _C aligned (for total internal reflection at A D ) where, _C= n₂ n₁ or _C= ⁻¹ ( n₂ n₁ ) (r₁ )_ =90^ - _C Now, applying Snell's law at face A B , we wet gathered n₁ n₂ = _ (r₁ )_ = _ (90- _C ) = _ _C _ = n₁ n₂ _C gathered aligned _ & = ⁻¹ [ n₁ n₂ _C ] & = ⁻¹ [ n₁ n₂ ( ⁻¹ ( n₂ n₁ ) ) ] aligned