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

For dark fringes of both waves at same place
`y_(1)=y_(2)`
`(n+1)(Dlamda_(1))/d=n(Dlamda_(2))/d`
or `(n+1)xx400=nxx560`
or n = 2.5, and n + 1 = 3.5
There integer value is 5 and 7.
The distance between two regions of complete dark,
`Deltax=7(Dlamda)/d=(7xx1xx400xx10^(-9))/(0.1xx10^(-3))=28mm`.