Two coherent light sources A and B with separation `2lambda` or placed on the x-axis symmetrically about the origin. They emit light of wavelength `lambda`. Obtain the positions of maxima on a circle of large radius, lying in the x-y plane and centre at the origin.

Explanation

For P to have maximum intensity , `d cos theta = n lambda `
` 2 lambda cos theta = n lambda cos theta =(n)/(2)` where n is integer
For ` n = 0 , theta = 90^(0) , 270^(0)`
`n = pm 1, theta = 60^(0) , 120^(0) , 240^(0), 300^(0)`
`n = pm 2, theta = 0^(0) , 180^(0)`
So, positions of maxima are at
`theta = 0^(0) , 60^(0), 90^(0), 120^(0), 180^(0), 240^(0), 270^(0) and 300^(0)`,
i.e., 8 positions will be obtained,
Short cut : In ` d = n lambda` then number of maximum on the circle is 4n . Not : For minima ,
`Delta x = (2n-1) (lambda)/(2)`