JEE Advanced 2016 · Paper 1 · Physics Q13

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PhysicsMultiple correct+4 / -2Question 13 of 54

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 $n_2\,(>n_1)$ , 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 horizontal slab of thickness d, shaded darker towards the bottom to show n(z) increasing downward (z measured down from the top). Above it is medium 1 (n₁ = constant), below it medium 2 (n₂ = constant). A ray enters the top surface at angle θᵢ to the vertical normal (dashed) and leaves the bottom surface at angle θ_f, displaced sideways by l from the incident normal.

n_1\sin\theta_i=n_2\sin\theta_f

n_1\sin\theta_i=(n_2-n_1)\sin\theta_f

l

is independent of

n_2

l

is dependent on

n(z)

Answer and worked solution

Official answer: A, C, D

Snell invariant. Treat the slab as many thin horizontal layers. At each boundary $n\sin\theta$ is unchanged, so
$n_1\sin\theta_i=n(z)\sin\theta(z)=n_2\sin\theta_f.$
(A) is true and (B) is false.

Lateral shift. The displacement $l$ is fixed by the path inside the slab:
$l=\int_0^d\tan\theta(z)\,dz.$
That depends on $n(z)$ (D is true) and not on the medium below (C is true).

(A), (C), (D)

Topics:Refraction at plane surfaces

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JEE Advanced 2016 · Paper 1, Physics question 13