Question

A monochromatic light wave is incident normally on a glass slab of thickness d, as shown in the figure. The refractive index of the slab increases linearly from n₁ to n₂ over the height h. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

(A) It will deflect up by an angle \(\tan^{-1} \left[\frac{(n_2^2 - n_1^2)d}{2h}\right]\)

(B) It will deflect up by an angle \(\tan^{-1} \left[\frac{(n_2 - n_1)d}h\right]\)

(C) It will not deflect

(D) The deflection angle depends only on (n₂ − n₁) and not on the individual values of n₁ and n₂

Answer 1

Dashed line MN and PQ are incident wave front.

Just before entering the slab PQ is maxima.

P₁ and Q₁ are the points on other face of slab.

So, P₁ will be at lead of n₂d w.r.t. P 

And Q' will be at lead of n1d w.r.t. Q

Right of the medium is homogeneous.

So to have same path lead as P₁.Q' must travel to Q₁, so n₂d = n₁d + h sin\(\theta\)