An interference is observed due to two coherent sources `S_1` placed at origin and `S_2` placed at `(0, 3lambda, 0)`. Here, lambda is the wavelength of the sources. A detector D is moved along the positive x-axis. Find x-coordinates on the x-axis (excluding `x = 0 and x= oo`) where maximum intensity is observed.

Explanation

At x = 0, path difference is `3lamda` . Hence, third order maxima will be obtained. At x = `oo` , path difference is zero. Hence, zero order maxima is obtained. In between, first and second order maximas will be obtained.

First order maxima:
` S_1P - S_1P = lamda " or " sqrt(x^2 + 9 lamda^2) - x = lamda `
or `sqrt(x^2 + 9 lamda^2) = x +lamda` Squaring both sides, we get `x^2 = 9lamdaa^2 = x^2 + lamda^2 + 2x lamda` Solving this, we get `x = 4 lamda`
Second order maxima: `S_2 P - S_1 P = 2 lamda`
or `sqrt(x^2 + 9 lamda^2) - x = 2 lamda " or " sqrt(x^2 + 9 lamda^2) = (x + 2 lamda)`
Squaring both sides, we get ` x^2 + 9 lamda^2 =x^2 +4 lamda^2 + 4x lamda`
Solving, we get` x = 5/4 lamda = 1.25 lamda`
Hence, the desired x coordinates are,
`x = 1.25 lamda` and x = `4 lamda`