Please solve this wave-optics based question?

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1 Answer
Mar 15, 2018

The condition will be #theta#= 4.(#lambda#/d)

Explanation:

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. #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 #theta# = Path difference / d =( 4.# lambda # /d )
or
#theta# = #Sin ^-1# (4#.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 #theta# as the angle

# 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 #theta#.