Question

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
(a) 4mm (b) 5.6mm (c) 14 mm (d)28 mm .
A. `4mm`
B. `5.6mm`
C. `14 mm`
D. `28 mm`

Answer 1

Correct Answer - D
Let nth minima of 400nm coincides with mth minima of 560nm, then
` ((2n-1)lambda_1 D)/(2d) = ((2n-1)lambda_2D)/(2d)`
or `(2n-1)(400/2)= (2m-1)(560/2)`
` (2n-1)/(2m-1)=7/5 = 14/10 =21/15`
If we take the first ratio, then n = 4 and m=3.
If we take the second ratio, then n =7.5 and m=5.5
This is not acceptable. If we take the ratio, then n= 11 and m=8
i.e. 4th minima of 400nm coincides with 3rd minima of 560nm.
Location of this minima is
`y_1= ((2xx 11-1)(1000)(400 xx 10^-6))/(2 xx 0.1) = 14 mm `.
Next 11 th minima of 400nm will coincide with 8th minima of 560nm.
Location of this minima is
` y_2 = ((2xx 11-1)(1000)(400 xx 10^-6))/(2xx0.1)) = 42mm.`
`:.` Required distance = `y_2- y_1 =28mm `
` :.` The correct option is (d) .