Intensity due to line source `S_(1)` at a distance of `r` is `I_(0)` and intensity due to other line source `S_(2)` at a distance of `r` is `4I_(0)` and frequency of both source are equal. If interference occurs at a point `P` as shown in the figure and wavelength of both sources is `r`, find the resultant intensity (in `watt//m^(2)`) at `P`. (where `I_(0)=2 "watt"//m^(2)`)

Options

A. `8`
B. `4`
C. `2`
D. `1`

Explanation

In case of line source `I prop 1//r`
Path difference `Deltax=4r-r=3r=3lambda`
So constructive interference occurs at `P`.
`I_(P)=I_(max)=(sqrt(I_(1))+sqrt(I_(2)))^(2)=4I_(0)`