JEE Advanced 2016 · Paper 2 · Physics Q13

← JEE Advanced 2016 · Paper 2

PhysicsMultiple correct+4 / -2Question 13 of 54

While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the $x$ - $y$ plane containing two small holes that act as two coherent point sources $(S_1,S_2)$ emitting light of wavelength 600 nm. The student mistakenly placed the screen parallel to the $x$ - $z$ plane (for $z>0$ ) at a distance $D=3$ m from the mid-point of $S_1S_2$ , as shown schematically in the figure. The distance between the sources $d=0.6003$ mm. The origin O is at the intersection of the screen and the line joining $S_1S_2$ . Which of the following is(are) true of the intensity pattern on the screen?

Two point sources S₁ and S₂, a distance d apart, lie on a hatched opaque plate along the y-axis, each emitting spherical wavefronts (dashed arcs). A screen stands perpendicular to the y-axis, in the x-z plane for z > 0, at distance D from the midpoint of S₁S₂; O is where the line S₁S₂ meets the screen, with the x-axis pointing out of the page and z upward.

Straight bright and dark bands parallel to the

x

-axis

The region very close to the point O will be dark

Hyperbolic bright and dark bands with foci symmetrically placed about O in the

x

-direction

Semi circular bright and dark bands centered at point O

Answer and worked solution

Official answer: B, D

At O. The screen is perpendicular to the line $S_1S_2$ , so at O the path difference is the full separation:
$\frac d\lambda=\frac{0.6003\times10^{-3}}{600\times10^{-9}}=1000.5.$
A half-integer number of wavelengths means a dark spot. (B) is true.

Fringe shape. Away from O, the path difference $d\cos\theta$ depends only on the angle from the axis $S_1S_2$ . Each fringe is therefore a circle centred on O. Only the half with $z>0$ is on the screen, so the bands are semicircles. (D) is true; (A) and (C) are false.

(B), (D)

Topics:Interference and Young's double slit

← Previous question Next question →

JEE Advanced 2016 · Paper 2, Physics question 13