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 π /2 at point P and π at point Q. Then the difference between the resultant intensities at P and Q will be: (a) 2 I (b) 6 I (c) 5 I (d) 7 I

Answer: (b). IR = I₁ + I₂ + 2√(I₁ I₂)cos φ, with 2√(9I²) = 6I. At P ( φ = π/2): IP = 10I. At Q ( φ = π): IQ = 4I. IP - IQ = 6I. So the answer is (b) 6I.

The two light beams having intensities I and 9I interfere to produce… | JEE Main 2022 (25 Jun, Shift 1)

Q70JEE Main 2022 · 25 JUN · SHIFT 1Medium

Superposition, Coherence & Intensity

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 $\pi$ /2 at point P and $\pi$ at point Q. Then the difference between the resultant intensities at P and Q will be:

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Answer: (b)

$I_R = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi$ , with $2\sqrt{9I^2} = 6I$ .
At $P$ ( $\phi = \pi/2$ ): $I_P = 10I$ . At $Q$ ( $\phi = \pi$ ): $I_Q = 4I$ .
$I_P - I_Q = 6I$ . So the answer is (b) $6I$ .

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