In young's double-slit experiment, the slit are 2 mm apart and are illuminated with a mixture ot two wavelengths `lambda_(0) = 750 nm` and `lambda = 900 nm`, The minimum distance from the common central bright fringe on a screen 2 m from the slits, where a bright fringe from one interference pattern coincides with a bright fringe from the other, is

Options

A. 6 mm
B. 12 mm
C. 8 mm
D. 9 mm

Answer

D

Explanation

The `m^(th)` bright fringe of the `lambda` pattern and the `n^(th)` bright fringe of the `lambda` pattern are located at
`y_(m) = (mDlambda)/(d)` and `y_(m)' = (n'D'lambda')/(d)` ltbr. Equating them `(m)/(n) = (6)/(5)`
Hence the first position at which overlaping occure is
`y_(6) = y_(5)' = (6 xx 2 xx 750 xx 10^(-9))/(1 xx 10^(-3)) m = 9 mm`