White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is b and the screen is at a distance d`(gtb) from the slits. At a point on the screen directly in front of one of the slits, certain wavelength are missing. Some of these missing wavelength are

Options

A. `lambda = (b^(2))/(d)`
B. `lambda = (2b^(2))/(d)`
C. `lambda = (b^(2))/(3 d)`
D. `lambda = (2 b^(2))/(3 d)`

Answer

A, C

Explanation

In Fig. point `P` is front of slit `A`. For missing wavelength, interference at `P` must be destructive :
`(x d)/(D) = (2n - 1)(lambda)/(2)`
Put `x = b//2, d = b` and `D = d`
`(b b)/(2d)=(2n-1)(lambda)/(2)=(lambda)/(2)` or `(3lambda)/(2)`
(when `n = 1 or n = 2`)

`:. lambda = (b^(2))/(d) , (b^(2))/(3 d)`