In YDSE bi-chromatic light of wavelengths 400 nm and 560 nm are used. The distance between the slits is `0.1` mm and the distance between the plane of the slits and the screen is 1.0m. The minimum distance between two successive regions of complete darkness is

Explanation

Let nth minimum of 400 nm coincides with mth minima of 560 nm, then
`(2n-1)((400)/(2))= (2 m-1)((560)/(2))" or "(2n-1)/(2m-1)= (7)/(5)= (14)/(10)="……."`
i.e., 4th minima of 400 nm coincides with 3rd minima of 560 nm. Location of this minima is,
`Y_(1)= ((2xx4-1)(1000)(400xx 10^(-9)))/(2xx 0.1)= 14 mm`
Next 11th minima of 400 nm will coincide with 8th minima of 560 nm.
Location of this minima is,
`Y_(2)= ((2xx 11-1)(1000)(400xx 10^(-9)))/(2xx0.1)= 42 mm`
Required distance `Y_(2)-Y_(1)= 28mm`.