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

Answer: (B), (D)

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

Answer 2

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]
$tan\theta=\frac{(n_2-n_1)d}{n}\Rightarrow \theta=tan^{-1}\frac{(n_2-n_1)d}{h}$