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 to over the height . Which of the following statement(s) is(are) true about the light wave emerging out of the slab?
\(t=\frac{d}{\frac{c}{n_1}}=\frac{n_1 d}{c}\)
in time t wavefront at B travel \(\mathrm{S}_1 ; S_1=\frac{c}{n_2} \times \frac{n_1 d}{c} \Rightarrow \frac{d n_1}{n_2}\)
When the wave front of \(\mathrm{B}\) reaches at the end of the slab then \(\mathrm{t}_1=\left(\frac{d-s_1}{c}\right) n_2 \Rightarrow \frac{d\left[n_2-n_1\right]}{c}\) in \(\mathrm{t}_1\) time, wavefront at \(\mathrm{A}\) travel \(\Rightarrow \mathrm{S}_2\)
\(\begin{aligned}
& \mathrm{S}_2=\mathrm{ct}_1=\mathrm{d}\left[\mathrm{n}_2-\mathrm{n}_1\right] \\
& \tan \theta=\frac{\left(n_2-n_1\right) d}{n} \Rightarrow \theta=\tan ^{-1} \frac{\left(n_2-n_1\right) d}{h}
\end{aligned}\)Asked in: JEE Advanced 2023 (Paper 2)