Two coherent light sources A and B are at a distance `3lambda` from each other `(lambda`=wavelength)The distances from A on the X-axis at which the interference is constructive are

Options

A. `3lambda`
B. `8lambda`
C. `5lambda//4`
D. `8.75 lambda`

Answer

C

Explanation

Say P be the point on X axis where constructive interference is obtained

`BP-AP=2lambda or lambda`
`:.sqrt(9lambda^(2)+x^(-2))-x=2lambda`
`:. 9lambda^(2)X^(2)=x^(2)+4lambda^(2)+4xlambdarArrx=(5lambda)/4`
Further, `sqrt(9lambda^(2)+x^(2))-x=lambda`
`:. 9lambda^(2)+x^(2)=x^(2)+lambda^(2)+2xlambda`
`:. x=4lambda`