In Young's double slit experiment , fringes of width `beta` are produced on a screen kept at a distance of 1 m from the slit . When the screen is moved away by `5 xx 10^(-2)` m , fringe width changes by `3 xx 10^(-5) `m . The separation between the slits is `1 xx 10^(-3)` m . The wavelength of the light used is ....nm

Options

A. 500
B. 600
C. 700
D. 400

Answer

B

Explanation

`beta = (lambda D)/(d) " " … (i)`
`beta' = (lambda D')/(d) " " … (ii)`
Subtract (ii) from (i) , we get
`beta - beta' = (lambda (D - D'))/(d)`
Substituting the given values , we get `3 xx 10^(-5) m = (lambda xx 5 xx 10^(-2) m)/(1 xx 10^(-3) m)`
`lambda = (3 xx 10^(-8))/(5 xx 10^(-2)) "" m = 0.6 xx 10^(-6)` m
`= 600 xx 10^(-9) m = 600` nm