JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Wave Optics

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The ratio of intensities at two points P and Q on the screen in a Young's double slit experiment where phase difference between two wave of same amplitude are

π /3

and

π /2

, respectively are

(A) $1 : 3$
(B) $3 : 1$
(C) $3 : 2$ ✓ Correct
(D) $2 : 3$

Answer: (C)

Solution

For two waves of equal amplitude

I_{0}

, the resultant intensity is

I = I_{0} + I_{0} + 2 I_{0} I_{0} cos ϕ = 2 I_{0} (1 + cos ϕ)

. At point P with

ϕ = π /3

I_{P} = 2 I_{0} (1 + cos (π /3)) = 2 I_{0} (1 + 1/2) = 3 I_{0}

. At point Q with

ϕ = π /2

I_{Q} = 2 I_{0} (1 + cos (π /2)) = 2 I_{0} (1 + 0) = 2 I_{0}

. The ratio

I_{P} : I_{Q} = 3 I_{0} : 2 I_{0} = 3 : 2

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Single correct option

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