In YDSE, bichromatic 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 1m. The minimum distance between two
successive regions of complete darkness is

Options

A. 4mm
B. 5.6mm
C. 14mm
D. 28mm

Answer

D

Explanation

Let `n^(th)` minima of 400 nm coincides with `m^(th)` minima of 560 nm, then
`(2n-1)((400)/(2))=(2m-1)((560)/(2))`.
or `(2n-1)/(2m-1)=(7)/(5)=(14)/(10)=(21)/(15)`= . . .
i.e., `4^(th)` minima of 400 nm coincides with 3rd minima of 560 nm. location of this minima is,
`Y_(1)=((2xx4-1)(1000)(400xx10^(-6)))/(2xx0.01)=14mm`
Next 11th minima of 400 nm will coincide with 8th minima
of 560 nm. location of this minima is,
`Y_(2)=((2xx11-1)(1000)(400xx10^(-6)))/(2xx0.01)=42mm`
`therefore`Required distance`=Y_(2)-Y_(1)=28mm`