Question

Two coherent radio-frequency point sources separated by `2.0 m` are radiating in phase with `lambda=0.50 m`. A detector moves in a circuit of large radius around the two sources in a plane containing them as shown in figure. Find (a) the angular position of interference maxima for `0lethetale90^(@)` and (b) number of maximum in the range `(-pi/2)lethetalepi/2` and in one complete rotation.

Answer 1

Path difference
`Deltax=d cos theta`
For maxima
`Deltax=nlambda implies d cos theta=nlambda`
`2 costheta=nxx1/2 implies costheta=n/4`
`n=0, theta=90^(@)`
`n=1, theta=cos^(-1)(1//4)`
`n=2, theta=60^(@)
n=3, theta=cos^(-1)(3//4)
n=4, theta=0^(@)`
(b)
`-pi/2lethetalepi/2`, number of maxima `=9`
In complete cercle, number of maxima `=16`