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
- A. The phase difference between the two rays is independent of d .
- B. The two rays interfere constructively at the detector.
- C. The phase difference between the two rays depends on n 1 but is independent of n 2
- 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
Practice more on Quantrex App →
Related: Physics — Wave Optics · All PYQ Banks