Two coherent sources separated by distance d are radiating in phase having wavelength `lambda`. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of `n=4` interference maxima is given as

Options

A. `"sin"^(-1) (nlambda)/d`
B. `"cos"^(-1) (4lambda)/d`
C. `"tan"^(-1)d/(4lambda)`
D. `"cos"^(-1)lambda/(4d)`

Answer

B

Explanation

Path difference at a point Q on the circle is

`Deltay=dcos theta`
For maxima at Q path difference should be integer multiple of wavelength
`Deltay=nlambda`
From Eqs. (i) and (ii)
`nlambda=dcos theta`
`:. theta=cos^(-1)((nlambda)/d)`
For `n=4`
Angular position `theta=cos^(-1) ((4lambda)/d)`