The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{\pi}{2}$ at point P and $\pi$ at point Q. Then the difference between the resultant intensities at P and Q will be:

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Wave Optics

The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is

\frac{π}{2}

at point P and

π

at point Q. Then the difference between the resultant intensities at P and Q will be:

(A)2I
(B)6I✓ Correct
(C)5I
(D)7I

Answer: (B)

Solution

The resultant intensity from two interfering beams is given by

I_{res} = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ

, where

ϕ

is the phase difference.

At point P (

ϕ = π /2

I_{P} = I + 9 I + 2 I \times 9 I cos (π /2) = 10 I + 0 = 10 I

At point Q (

ϕ = π

I_{Q} = I + 9 I + 2 I \times 9 I cos π = 10 I + 6 I (- 1) = 10 I - 6 I = 4 I

Therefore,

I_{P} - I_{Q} = 10 I - 4 I = 6 I

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Single correct option

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