JEE Advanced 2022 · Paper 2 · Physics Q13

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PhysicsMultiple correct+4 / -2Question 31 of 54

A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index $n_2$ . The other slit is at the interface of this medium with another medium 1 of refractive index $n_1\ (\neq n_2)$ . The line joining the slits is perpendicular to the interface and the distance between the slits is $d$ . The slit widths are much smaller than $d$ . A monochromatic parallel beam of light is incident on the slits from medium 1. A detector is placed in medium 2 at a large distance from the slits, and at an angle $\theta$ from the line joining them, so that $\theta$ equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.

Which of the following statement(s) is(are) correct?

Medium 1 (index n1) above, medium 2 (index n2) below, separated by a horizontal interface. A parallel beam comes in obliquely from medium 1. A vertical opaque screen has one slit at the interface and a second slit a distance d below it in medium 2 (the line joining the slits is perpendicular to the interface). A detector in medium 2 is far away along a direction at angle θ to the line of the slits.

The phase difference between the two rays is independent of

d

The two rays interfere constructively at the detector.

The phase difference between the two rays depends on

n_1

but is independent of

n_2

The phase difference between the two rays vanishes only for certain values of

d

and the angle of incidence of the beam, with

\theta

being the corresponding angle of refraction.

Answer and worked solution

Official answer: A, B

Before the slits. The beam refracts into medium 2 at the angle $\theta$ , with $n_1\sin i=n_2\sin\theta$ , measured from the normal, which is the line of the slits. Light reaching the lower slit travels an extra $d\cos\theta$ in medium 2: an extra optical path of $n_2d\cos\theta$ .

After the slits. The detector is at angle $\theta$ from the line of the slits, in medium 2. Toward it, the ray from the upper slit travels the extra $d\cos\theta$ , again in medium 2.

Net. The two extra paths cancel, so the phase difference is zero for every $d$ , $n_1$ and $n_2$ .

(A) True.
(B) True: the rays interfere constructively.
(C) False.
(D) False.

(A), (B).

Topics:Interference and Young's double slit Refraction at plane surfaces

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JEE Advanced 2022 · Paper 2, Physics question 13