JEE Advanced 2019 · Paper 2 · Physics Q7

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PhysicsMultiple correct+4 / -1Question 7 of 54

In a Young's double slit experiment, the slit separation $d$ is 0.3 mm and the screen distance $D$ is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle $\alpha$ as shown in figure. On the screen, the point $O$ is equidistant from the slits and distance $PO$ is 11.0 mm. Which of the following statement(s) is/are correct?

A parallel beam arrives from the upper left at angle α to the axis and falls on two slits a distance d apart; the screen is a distance D away. O on the screen is on the axis, equidistant from the slits, and P is above O.

For

\alpha = \dfrac{0.36}\pi

degree, there will be destructive interference at point

O

For

\alpha = 0

, there will be constructive interference at point

P

For

\alpha = \dfrac{0.36}\pi

degree, there will be destructive interference at point

P

Fringe spacing depends on

\alpha

Answer and worked solution

Official answer: C

Path difference. The oblique beam reaches the upper slit first, adding $d\sin\alpha$ . A point at height $y$ on the screen adds $dy/D$ :
$\Delta=d\sin\alpha+\frac{dy}D.$

Numbers.

$\alpha=\frac{0.36}\pi$ degree $=0.002$ rad, so $d\sin\alpha=0.3\text{ mm}\times0.002=0.6\ \mu$ m $=\lambda$ .
At P, $\dfrac{dy}D=\dfrac{0.3\times11}{1000}$ mm $=3.3\ \mu$ m $=5.5\lambda$ .

The options.

(A) At O, $\Delta=\lambda$ : constructive, not destructive. False.
(B) With $\alpha=0$ , at P $\Delta=5.5\lambda$ : destructive. False.
(C) With $\alpha=\frac{0.36}\pi$ degree, at P $\Delta=6.5\lambda$ : destructive. True.
(D) The fringe width $\lambda D/d$ does not depend on $\alpha$ . False.

(C)

Topics:Interference and Young's double slit

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JEE Advanced 2019 · Paper 2, Physics question 7