A transparent slab of thickness d has a refractive index n (z) that...

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 $l$ . Which of the following statement(s) is (are) true?
$A transparent slab of thickness d has a refractive index n (z) that increases with z. Here z is the vertical distance$

Options

A $l$ is independent of ${n}_{2}$
B $l$ is dependent on n (z)
C ${n}_{1}sin {\theta}_{i} = \left({n}_{2} - {n}_{1}\right)sin {\theta}_{f}$
D ${n}_{1}sin {\theta}_{i} = {n}_{2}sin {\theta}_{f}$

Correct answer

A. $l$ is independent of ${n}_{2}$

Step-by-step solution

For parallel slab

{n}_{1}sin {\theta}_{i} = {n}_{2}sin {\theta}_{f}

And

l

depends on refractive angle in slab

∴ l

depends on refractive index of slab and independent of

{n}_{2}

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