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In Young's experiment, the wavelength of monochromatic light used in 6000Å. The optical path difference between the rays from the two coherent sources are 0.0075 mm and 0.0015 mm at points P and Q, respectively, onthe screen and on opposite sides of the central bright band. How many bright and dark bands are observed between points P and Q? |
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Answer» <P> Solution :Data: `Delta_(1) = 7.5 xx 10^(-6)m, Delta_(2) = 1.5 xx 10^(-6)m, lambda=6 xx 10^(-7)m`For point P: Let p be an integer such that `p(lambda/2) = Delta_(1)` `THEREFORE p = (2Delta_(1))/(lambda) = (2 xx 7.5 xx 10^(-6))/(6 xx 10^(-7)) = 150/6=25` `therefore` The path difference `Delta_(i)` is an odd integral multiple of `lambda/2, Delta_(1) = (2m-1)lambda/2`, where m is an integer. `therefore 2m-1=25 therefore m=13` `therefore` Point P is on the 13th dark band. For point Q: Let q be an integer such that `q lambda/2= Delta_(2)`, `therefore = (2Delta_(2))/(lambda) = (2 xx 1.5 xx 10^(-6))/(6 xx 10^(-7)) = 30/6 = 5` `therefore` the path difference `Delta_(2)` is an odd integral multiple of `lambda/2`, `Delta_(2) = (2n-1)lambda/2`, where n is an integer. `therefore 2n-1=5 therefore n=3` `therefore` Point Q is on the 3rd dark band. Betwen points P and Q, excluding the bonds at these points, the NUMBER of dark bonds `=12+2=14` and the number of BRIGHT bands (including the central bright band) `=12+2+1=15` |
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