    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 S1S2. Find the position of farthest minima. A
D=λ2
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B
D=15λ12
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C
D=15λ4
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D
D=λ3
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Solution

## The correct option is C D=15λ4 The maximum and minimum path difference between the waves are, 2λ (when point P is very close to S2) and zero (when point P is at infinity), respectively. For any minima, the path difference is equal to odd multiple of λ2. ∴ Only two minima obtained from S2 till infinity, along the line S2P. Close to S2, the path difference is 2λ. As we move away from S2, along the line S2P, the path difference starts to decrease. ∴ The farthest minima will have a path difference λ/2 and the nearest minima will have a path difference of 3λ2. Now, for the farthest minima, S1P−S2P=λ2 ⇒√4λ2+D2−D=λ2 4λ2+D2=(D+λ2)2 ⇒4λ2+D2=λ24+D2+Dλ ⇒D=4λ−λ/4=15λ4 Hence, (C) is the correct answer.  Suggest Corrections  0    Join BYJU'S Learning Program  Related Videos   Intensity of Sound
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