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

Options

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

Answer

A

Explanation

Path difference between the rays reaching infront of slit `S_1` is.

`S_1P-S_2P=(b^2+d^2)^(1//2)-d`
For destructive interference at P
`S_1P-S_2P=((2n-1)lambda)/(2)`
i.e., `(b^2+d^2)^(1//2)-d=((2n-1)lambda)/(2)`
`impliesd(1+b^2/d^2)^(1//2)-d=((2n-1)lambda)/(2)`
`impliesd(1+(b^2)/(2d^2)+...)-d=((2n-1)lambda)/(2)`
(Binomial Expansion)
`(b)/(2d)=((2n-1)lambda)/(2)implieslambda=(b^2)/((2n-1)d)`
For `n=1, 2, 3,...., lambda=b^2/d, (b^2)/(3d)`