In the figure below, P and Q are two equally intense coherent sources… | JEE Main 2020 (6 Sep, Shift 1)

Q87JEE Main 2020 · 6 SEP · SHIFT 1Difficult

Superposition, Coherence & Intensity

In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m. The separation between P and Q is 5 m and the phase of P is ahead of that of Q by 90°. A, B and C are three distinct points of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:

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Answer: (b)

$PQ = 5\text{ m} = \frac{\lambda}{4}$ , so the extra path $PQ$ adds a phase lag of $\frac{\pi}{2}$ .
At A (beyond Q): wave from P travels $\frac{\lambda}{4}$ more, lag $\frac{\pi}{2}$ cancels P's lead of $\frac{\pi}{2}$ : $\phi = 0$ , $I_A = 4I_0$ .
At B (on the bisector): equal paths, $\phi = \frac{\pi}{2}$ , $I_B = 4I_0\cos^2 45^\circ = 2I_0$ .
At C (beyond P): wave from Q travels $\frac{\lambda}{4}$ more, total $\phi = \frac{\pi}{2} + \frac{\pi}{2} = \pi$ , $I_C = 0$ .
$I_A : I_B : I_C = 4 : 2 : 0 = 2 : 1 : 0$ , so the answer is (b).

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Superposition, Coherence & Intensity question from JEE Main 2020 (6 Sep, Shift 1)

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