JEE Advanced 2023 · Paper 2 · Physics Q5

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PhysicsMultiple correct+4 / -2Question 22 of 51

A monochromatic light wave is incident normally on a glass slab of thickness $d$ , as shown in the figure. The refractive index of the slab increases linearly from $n_1$ to $n_2$ over the height $h$ . Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

$A plane monochromatic light wave (horizontal rays with vertical dashed wavefronts) travels to the right towards a vertical glass slab of thickness d. Over the height h of the slab the refractive index increases linearly from n1 at the bottom to n2 at the top (n2 > n1), shown by darker shading towards the top.$

It will deflect up by an angle

\tan^{-1}\left[\dfrac{(n_2^2-n_1^2)d}{2h}\right]

It will deflect up by an angle

\tan^{-1}\left[\dfrac{(n_2-n_1)d}{h}\right]

It will not deflect.

The deflection angle depends only on

(n_2 - n_1)

and not on the individual values of

n_1

and

n_2

Answer and worked solution

Official answer: B, D

Optical path. At height $y$ the index is $n(y)=n_1+\frac{(n_2-n_1)y}{h}$ . The optical path through the slab is $n(y)\,d$ .

Tilt of the wavefront. Across the height $h$ the optical path differs by $(n_2-n_1)d$ , so the emerging wavefront is tilted. The ray turns towards the larger index (upwards) by an angle $\theta$ with
$h\sin\theta=(n_2-n_1)d.$

Options.

For a thin slab ( $d\ll h$ ) the angle is small, so $\tan\theta\approx\sin\theta=\frac{(n_2-n_1)d}{h}$ . (B) is correct.
(A) and (C) are wrong.
(D) is correct: the angle depends only on $n_2-n_1$ .

Topics:Huygens' principle Refraction at plane surfaces

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JEE Advanced 2023 · Paper 2, Physics question 5