Problem 9. Two sources S, and S, em...

Problem 9. Two sources S, and S, emitting light of wavelength 600 nm are placed 0.1 mm apart. A detector is moved on the line SP which is perpendicular to SS2 (i) What would be the minimum and maximum path difference at the detector as it is moved along the line S,P. (ii) Locate the position of farthest minimum detected.

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Solution. (i) The situation is shown in ( mathrm{Fig} ). 10.65 The path difference is minimum when the detector is at large distance from ( S_{1} ). Then the path difference is near to zero. Fig. 10.65 The path difference is maximum when the detector lies at point ( S_{1} ) ( therefore ) Maximum path difference ( =S_{1} S_{2}=0.1 mathrm{mm} ) (ii) The farthest minimum will occur at a point ( P ) for which the path difference is ( frac{lambda}{2} ) Let ( S_{1} P=D ). Then [ p=S_{2} P-S_{1} P=frac{lambda}{2} ] or ( sqrt{D^{2}+d^{2}}-D=frac{lambda}{2} ) or ( D^{2}+d^{2}=left(D+frac{lambda}{2}right)^{2} )
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