Two source are placed on x-axis at a separation `d = 3lambda`. An observer starts moving from A on a circular track of radius R `(R gt gt d)`. How many bright points and dark points will he observer?
Find the angular positions of maxima and minima.
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Explanation

The observer will have maximum path difference at position A and C equal to `3 lambda`
Minimum path difference equals to zero at position B and D.
In each quarter circle, he will have path difference between 0 and `3 lambda`
path difference corresponding to maxima in our given range is 0, `lambda, 2 lambda, 3 lambda`.
Path difference corresponding to minima inour given range is `lambda//2, 3 lambda//2, 5 lambda//2`.
Hence total number of bright point in the complete circular path is `4 xx 2 + 4 = 12`.
Total number of dark points on circular path is `4 xx 3 = 12`.
Hence, the observer will find 12 bright points and 12 dark points in the circular track.
Finding angular positions of maxima and minima:
Path difference at point P.
`S_(1)P -S_(2)P = Delta x`
` S_(1) A = Delta x`
`d cos theta = Delta x`
Hence, `cos theta = (lambda D)/(4d)`
`implies theta = cos^(-1) ((Delta x)/(d))`
For Maxima, `Delta x = n lambda`
For minima,`Delta x = (2n - 1)(lambda)/(2)`
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