Please solve this wave-optics based question?

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Answer 1 · 2018-03-15T21:03:32

The condition will be $θ$ $theta$ = 4.( $λ$ $lambda$ /d)

In the present interference problem with two coherent sources

the distance between the coherent sources is d

and the detector moves on a very big circle

so the place of detection can be taken as distance D from the sources

The condition for maxima ,

path diff = n. $λ$ $lambda$

here n=4 and

if one draws a perpendicular from the 2nd source(on the right )

to the line joining the 1st source(on the left) to 4th maxima then the path difference will be equal to

base of the triangle formed with theta as vertical angle and d as the hypotenuse

therefore the angular displacement from the central maxima of

the fourth bright spot can be written as

Sin $θ$ $theta$ = Path difference / d =( 4. $λ$ $lambda$ /d )
or
$θ$ $theta$ = ${sin}^{- 1}$ $Sin ^-1$ (4 $. λ$ $.lambda$ /d )

and D is much larger compared to d ,

the fringes can be taken on an arc of circle D.

The angular displacement of the detector will be same angle $θ$ $theta$ as the angle

$θ$ $theta$ = (arc length from central to 4th maxima)/D

as D is very large the radius drawn from the two coherent sources to the 4th maxima will turn through same angle $θ$ $theta$ .