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 ≠

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 $n_{1} (\neq n_{2})$ . 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 $θ$ 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.

Screenshot 2026-02-08 at 8.55.17 PM.png

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

TestHub · Accepted Answer

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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