Optics 2 Question 17
17. A transparent slab of thickness $d$ has a refractive index $n(z)$ that increases with $z$. Here, $z$ is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices $n _1$ and $n _2\left(>n _1\right)$, as shown in the figure. A ray of light is incident with angle $\theta _i$ from medium 1 and emerges in medium 2 with refraction angle $\theta _f$ with a lateral displacement $l$.
(2016 Main)
Which of the following statement(s) is (are) true? (a) $l$ is independent on $n(z)$
(b) $n _1 \sin \theta _i=\left(n _2-n _1\right) \sin \theta _f$
(c) $n _1 \sin \theta _i=n _2 \sin \theta _f$
(d) $l$ is independent of $n _2$
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Answer:
Correct Answer: 17. (a, c, d)
Solution:
- From Snell’s law,
$n \sin \theta=$ constant
$\therefore n _1 \sin \theta _i=n _2 \sin \theta _f$
Further, $l$ will depend on $n _1$ and $n(z)$. But it will be independent of $n _2$.
