In a Young's doule slit experiment, the slits are 2 mm apart and are illuminated with a mixture of two wavelengths `lamda=750nm` and `lamda'=900nm`. At what distance from the common central bright fringe on a screen 1.5 m from the slits will a bright fringe from one interference pattern coincide with a bright fringe from the other?

Explanation

The `n^(th)` bright fringe of the `lambda` pattern and the `n^(th)` bright fringe of the `lambda` pattern are situated at `yn=n(Dlambda)/(d)` and `yn.=n.(Dlambda.)/(d)`
As this coincide, yn=yn.
`implies(nDlambda)/(d)=(n.Dlambda.)/(d)`
`implies(n)/(n.)=(lambda.)/(lambda)=(900)/(750)=(6)/(5)`
hence the first position where overlapping occur is `y_(5)=y_(6)=(nDlambda)/(d)=(6(2m)(750xx10^(-9)m))/((2xx10^(-3)m))=4.5mm`