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Question

Two coherent point sources S1 and S2, vibrating in phase, emit light of wavelength λ. The separation between the sources is 2λ. Consider a line passing through S2 and perpendicular to the line S1 S2. What is the smallest distance from S2 where a minimum intensity occurs?

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Solution



Let P be the point of minimum intensity.
For minimum intensity at point P,

S1P-S2P=x=2n+1 λ2

Thus, we get:

Z2+2λ2-Z=2n+1 λ2Z2+4λ2=Z2 2n+12 λ24+2Z 2n+1 λ2Z=4λ2-2n+1 2λ2/42n+1 λ =16λ2-2n+14 2n+1 λ ... (i)

When n=0, Z=15λ4 n=-1, Z=-15λ4 n=1, Z=7λ12 n=2 , Z=-9λ20

Thus, Z=7λ12 is the smallest distance for which there will be minimum intensity.

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