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

Answer

9

Explanation

The `m^(th)` bright fringe of the `lamda` pattern and the `n^(th)` bright fringe of the `'lamda'` pattern are located at
`y_(m)=(mDlamda)/d` and `y_(m)=(n^(')Dlamda^('))/d`
Equating them `m/n=6/5`
Hence the first positon at which overlaping occurs is
`y_(6)=y_(5)^(')=(6xx2xx750xx10^(-9))/(1xx10^(-3))m=9mm`