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 `3lambda`. 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 maxima will be obtained.

First order maxima:
`S_(2)P-S_(1)P= lambda (or) sqrt(x^(2)+9lambda^(2))- x=lambda`
or `sqrt(x^(2)+9lambda^(2))= x+lambda` Squaring both sides, we get `x^(2)+9lambda^(2)=x^(2)+lambda^(2)+2xlambda`. Solving this, we get `x =4lambda`. Second order maxima: `S_(2)P-S_(1)P= 2lambda, (or) sqrt(x^(2)+9lambda^(2))-x=2lambda (or) sqrt(x^(2)+9lambda^(2))= (x+2lambda)` Squaring both sides, we get
`x^(2)+9lambda^(2)= x^(2)+4lambdas^(2)+4xlambda`
Solving, we get `x = (5)/(4)lambda = 1.25 lambda`
Hence, the desired x coordinates are, `x = 1.25lambda and x = 4lambda` .