A beam of light consisting of two wavelengths `650 nm` and `520 nm` is used to obtain interference fringes in a Young's double slit experiment.
(a) Find the distance of the third bright fringe on the screen from the central maximum for the wavelength `650 nm`.
(b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide? The distance between the slits is `2 mm` and the distance between the plane of the slits and screen is `120 cm`.

Explanation

`lambda_(1)=650 nm, lambda_(2)=520 nm`
`d=2 mm, D=120 cm`
(a) For wavelength `lambda_(1)=650 nm`
Distance of `3^(rd)` gright fringe
`y_(3)=(nDlambda_(1))/d=(3xx1.2xx650xx10^(-9))/(2xx10^(-3))`
`=1170xx10^(-6) m=1.17xx10^(-3)m=1.17 mm`
(b) Let `p^(th)` bright fringe due to `lambda_(1)` coincides with `q^(th)` bright fringe due to `lambda_(2)`.
`y=(pDlambda_(1))/d=(qDlambda_(2))/d`
`p/q=lambda_(2)/almbda_(1)=520/650=4/5`
`y_(min)=(pDlambda_(1))/d=(4xx1.2xx650xx10^(-9))/(2xx10^(-3))=1/56 mm`