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(gtgtb)` from the slits. At a point on the screen directly in front of
one of the slits, certain wavelengths are missing. Some of these missing
wavelength are
`(a) lambda = b^2//d (b) lambda=2b^2//d (c) lambda = b^2//3d (d)lambda = 2b^2//3d ` .

Options

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

Answer

A, C

Explanation

At P (directly in front of `S_1`)y = b/2
:. Path difference, `Deltax = S_2 P - S_1 P = (y.(b)/d) = (((b/2)(b))/d) = b^2/2d`
Those wavelengths will be missing for which
` Delta x = lambda_1/2 , (3lambda_2)/2, (5lambda_3)/2`………
` lambda_1 = 2Deltax = b^2/d `
` lambda_2 = (2Deltax)/3 = b^2/(3d)`
` lambda_3 = (2Deltax)/5 = b^2/(5d)`
Therefore, the correct options are (a) and (c).