InterviewSolution
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InterviewSolution
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Two coherent point sources `S_(1)` and `S_(2)` vibrating in phase emit light of wavelength `lambda`. The separation between the sources is `2lambda`. Consider a line passing through `S_(2)` and perpendicular to line `S_(1) S_(2)`. Find the position of farthest and nearest minima.. |
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Answer» `Delta x_(min) = (2n-1) (lambda)/(2)` The farthest minima has path difference `lambda//2` while nearest minima has path difference `(3//2)lambda`. For the nearest minima. `S_(1)P-S_(2)P= (3)/(2)lambda`, (as maximum path difference is `2lambda`] `implies sqrt((2lambda)^(2)+D^(2)) - D=(3)/(2)lambda implies (2lambda)^(2)+D^(2)= ((3)/(2)lambda+ D)^(2)` `implies 4lambda^(2)+D^(2) = (9)/(4)lambda^(2)+D^(2)xx2xx(3)/(2)lambda xxD` `implies 3D = 4lambda- (9lambda)/(4) = (7lambda)/(4) implies D = (7)/(12) lambda` For the farthest minima, `S_(1)P-S_(2)P = (lambda)/(2)` `implies sqrt(4lambda^(2)+D^(2))-D = (lambda)/(2)` `implies 4 lambda^(2)+D^(2)= (lambda^(2))/(4)+D^(2)+Dlambda implies D= 4lambda-lambda//4 = (15lambda)/(4)` |
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