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

Here path difference at a point P on the circle is given by

`Deltax=dcostheta` …(i)
For maxima at P
`Deltax=nlambda` …(ii)
From equations (i) and (ii)
`nLambda=dcosthetaimpliesthetacos^-1((nlambda)/(d))=cos^-1((4lambda)/(d))`