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A ray of light travelling in air is incident at grazing incidence on a slab with variable refractive index, $n (y) = [k y^{3/2}+ 1]^{1/2}$ where $k = 1 m^{-3/2}$ and follows path as shown in the figure. What is the angle of refraction when the ray comes out.
enter image description here
$(A) 60^°$
$(B) 53^°$
$(C) 30^°$
$(D)$ No deviation

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My approach:-

Let the angle of emergence br $r$
At origin i. e $y=0$ $n_1=1$ and when $y=1$ $n_2=\sqrt2$
Using Snell's law $$n_1 \sin90^° = n_2 sinr $$ On solving this I get $r=45^°$ but the sad part is that my answer doesn't match with any option.

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closed as off-topic by ACuriousMind Apr 26 at 16:12

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  • $\begingroup$ The ray does not emerge into a medium of index $ \sqrt{2} $. $\endgroup$ – nasu Apr 26 at 16:01
  • $\begingroup$ So what index the ray emerge, I simply put y = 1 in given equation $\endgroup$ – Abhishek Kumar Apr 26 at 16:03
  • $\begingroup$ Please note that homework-like questions and check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions over those just asking for a specific computation. $\endgroup$ – ACuriousMind Apr 26 at 16:12
  • $\begingroup$ @Abhishek The ray emerges in air, according to your image. $\endgroup$ – nasu Apr 26 at 22:32
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Consider what the angle of emergence is if the slab has a non-varying refractive index. Then consider what happens if you stack two slabs with different index. Then you can extrapolate to a single slab with a continuously varying index.

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  • $\begingroup$ Because this appears to be a homework problem, I won't send the solution. All you get is the hint I gave in my answer. $\endgroup$ – S. McGrew Apr 26 at 16:37
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Answer is 4) No deviation . For a slab there is no deviation. $n_1=n_2=1$ of emergent ray from incident ray.

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  • $\begingroup$ How n1 and n2 =1 $\endgroup$ – Abhishek Kumar Apr 26 at 16:14
  • $\begingroup$ Both the incidence and emergence is in air. Doesn't matter what the slab is untill it has parallel opposite faces. It is asked clearly in the question the angle of emergence. $\endgroup$ – Tojrah Apr 26 at 16:23

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