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Two equally intense coherent sources P and Q emit waves of wavelength 20 m. They are separated by 5 m, and P leads Q in phase by 90 deg. Points A, B and C are three distinct observation points, each equidistant from the midpoint of PQ (one on the axis beyond P, one off-axis, one on the axis beyond Q). Find the ratio of intensities at A, B and C.

1. 0: 1: 2
2. 4: 1: 0
3. 0: 1: 4
4. 2: 1: 0

Correct answer: 0: 1: 4

Solution

Along the line of sources the path difference is 5 m = lambda/4 = 90 deg phase. Combined with the intrinsic 90 deg phase lead of P, on one side the phases add to 180 deg (destructive, I=0) and on the other side they cancel to 0 deg (constructive, I=4I0). Off-axis point B (equal distance from both) has only the intrinsic 90 deg difference giving intermediate intensity (2I0 -> normalized 1). Ratio 0: 1: 4.

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