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Question
In Young’s double slit experiment, the slits are separated by 0.5 mm and screen is placed 1.0 m away from the slit. It is found that the 5th bright fringe is at a distance of 4.13 mm from the 2nd dark fringe. Find the wavelength of light used.
Solution
Given d = 0.5mm
D = 1.0m
5th bright `x_n = ( n lambda D ) / d`
`x_5 = 5 ( lambda D) /d`
2nd dark `x_m = (2m-1) (lambdaD)/(2d)`
`5(lambdaD)/(d) = (3 lambdaD)/(2d) = 4.13 xx 10^(-3) ⇒ ( 7lambdaD)/(2d) = 4.13 xx 10^(-3)`
`(7lambda xx 1)/(2 xx5 xx10^(-4)) = 4.13 xx 10^(-3) lambda = (2 xx 4.13 xx 10^(-3) xx 5 xx 10^(-4))/7`
`lambda = 5.9 xx 10^(-7) m`
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