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ABC is a spherical wavefront centred at 'O' symmetric about BE is incident on slits S_(1) and S_(2) .BS_(1) = 3lambda , S_(1)S_(2) = 4 lambda , BO = 6lambda ,S_(1)E = 128 lambdaand lambdais the wavelength of incident light wave. A mica sheet of refractive index 1.5 is pated on S_(2). Find the minimum value of thickness of mica sheet for whhichcentral fringe forms at E ? |
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Answer» `(31lambda)/(8)` `S_(2)S_(2)+(mu - 1)t+S_(2)E = S_(1)^(1)S_(1)+S_(1)E` `implies(OS_(2)^(1)-OS_(2))+(mu-1)t+sqrt(D^(2)+d^(2)) = (OS_(1)^(1)-OS_(1))+D` `implies(mu-1)t = (OS_(2)-OS_(1))+(sqrt(D^(2)+d^(2))-D)` `implies(mu-1)t = 2lambda - [D(1+(d^(2))/(D^(2)))^(1//2)-D]` `implies2lambda - [D(1+(d^(2))/(2D^(2)))-D] implies 2 lambda - [D+(d^(2))/(2D)-D]` `(mu-1)t=2lambda - (d^(2))/(2D) ((3)/(2) - 1)t = 2xxlambda - (16lambda^(2))/(2xx128lambda)` `(1)/(2)t = 2lambda - (lambda)/(16) (1)/(2)t = (31lambda)/(16) = (31lambda)/(8)` Thickness of mica sheet `t = (31lambda)/(8)` |
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