Two coherent narrow slits emitting light of wavelength `lambda` in the same phase are placed parallel to each other at a small separation of `2lambda`. The light is collected on a screen S which is placed at a distance D(`gtgt lambda`) from the slit `S_1` as shown in figure. Find the finite distance x such that the intensity at P is equal to intensity O.
.

Options

A. `sqrt(3D)`
B. `sqrt(8)D`
C. `sqrt(5)D`
D. `sqrt(5)(D)/(2)`

Answer

B

Explanation

In this case path difference is d `costheta`.
so `nlamda=lamda=3lamdacosthetaimpliescostheta=(1)/(3)`
`implies(D)/(sqrt(D^(2)+y^(2)))=(1)/(3)implies3D=sqrt(D^(2)+Y^(2))`
`impliesy=sqrt(8)D=2sqrt(2)D`