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Two coherent sources separated by distan...

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

A

`"sin"^(-1) (nlambda)/d`

B

`"cos"^(-1) (4lambda)/d`

C

`"tan"^(-1)d/(4lambda)`

D

`"cos"^(-1)lambda/(4d)`

Text Solution

Verified by Experts

The correct Answer is:
B
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)`
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