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JEE Advanced Physics Wave Optics 2022 JEE Advanced 2022 (Paper 2)

JEE Advanced Physics Question (2022) — Solution

Question

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 ≠ 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 θ  from the line joining them, so that θ  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?

Options

  1. A. The phase difference between the two rays is independent of d .
  2. B. The two rays interfere constructively at the detector.
  3. C. The phase difference between the two rays depends on  n 1 but is independent of  n 2
  4. D. The phase difference between the two rays vanishes only for certain values of d and the angle of incidence of the beam, with  being the corresponding angle of refraction.

Answer

B. The two rays interfere constructively at the detector.

Step-by-step solution

From the above figure, A B = d tan θ and  B C = A B sin α = d tan θ sin α Also,  A D = A B sin θ ⇒  Path difference (in vaccum) = n 1 B C - n 2 A D = n 1 A B sin α - n 2 A B sin θ From snell's law  n 1 sin α = n 2 sin θ . Therefore, path difference = A B n 1 sin α - n 2 sin θ = 0 ⇒     A , B  are correct C , D  are incorrect

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