The slit plane contains 3 identical slits. P, Q, R are points on screen directly infront of the slits A, B, C. Intensity at any point on screen due to each slit is I 0 . ( λ is wavelength of light u

Question

The slit plane contains 3 identical slits. P, Q, R are points on screen directly infront of the slits A, B, C. Intensity at any point on screen due to each slit is $I_{0}$ . ( $λ$ is wavelength of light used) Initial phase at A, B and C is same.

List-I	List-II
(P) Intensity at P, if $\frac{d ^{2}}{D} = \frac{λ}{2}$	(1) $I_{0}$
(Q) Intensity at Q, if $\frac{d ^{2}}{D} = λ$	(2) $2 I_{0}$
(R) Intensity at Q, if slit B is closed and $\frac{d ^{2}}{D} = \frac{λ}{2}$	(3) $5 I_{0}$
(S) Intensity at mid-point of P and R, if $\frac{d ^{2}}{D} = λ$	(4) 0
	(5) $9 I_{0}$

TestHub · Accepted Answer

(P) At P ( d 2 / D = λ /2 ): path differences Δ A B ​ = 4 λ ​ , Δ A C ​ = 4 9 λ ​ ⇒ two amplitudes A at 90°, third in phase with one of them: I = 5 I 0 ​ → ( 3 ) (Q) At Q ( d 2 / D = λ ): Δ A B ​ = 2 λ ​ , Δ BC ​ = 2 λ ⇒ B cancels A, only C remains: I = I 0 ​ → ( 1 ) (R) B closed at Q: Δ A C ​ = 4 3 λ ​ × 2 = 2 3 λ ​ … ⇒ I = 2 I 0 ​ → ( 2 ) (S) Mid-point of P and R: A and C arrive in phase (Δ = λ and 0), B adds fully: I = 9 I 0 ​ → ( 5 ) Hence (B).

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