Question

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

Monochromatic light wave
 

• A. It will not deflect.
• B. It will deflect by an angle \(tan^{-1}[\frac{(n_2-n_1)d}{h}]\)
• C. The deflection angle depends only on (n₂ - n₁) and not on the indivisual values of n₁ and n₂
• D. It will deflect up by an angle \(tan^{-1}[\frac{(n_2^2-n_1^2)d}{2h}]\)

Answer 1

The Correct Option is B, D

The correct answers are (B) and (C).


\(t=\frac{d}{\frac{c}{n_1}}=\frac{n_1d}{c}\)
in time t wavefront at B travel S₁; \(S_1=\frac{c}{n_2}\times\frac{n_1d}{c}\Rightarrow\frac{dn_1}{n_2}\)
When the wave front of B reaches at the end of the slab then t₁ =\((\frac{d-s_1}{c})n_2\Rightarrow \frac{d[n_2-n_1]}{c}\)
in t₁ time, wavefront at A travel \(\Rightarrow\) S₂
S₂=ct₁=d[n₂-n₁]
\(tan\theta=\frac{(n_2-n_1)d}{n}\Rightarrow \theta=tan^{-1}\frac{(n_2-n_1)d}{h}\)
 

Answer 2

Dashed lines MN and PQ represent incident wave fronts.
 Just before entering the slab, PQ is at a maximum. 
Points P₁ and Q₁ are on the other side of the slab. 
Therefore, P₁ will be ahead by n₂​d compared to P, and Q₁ will be ahead by n₁​d compared to Q.
 The right side of the medium is homogeneous. 
To have the same path lead as P₁, Q' must travel to Q₁, so 𝑛₂𝑑=𝑛₁𝑑+ℎsin⁡𝜃.