Find the ratio of intensities at the two points `X and Y` on a screen in Young's double slit experiment, where waves from the two source `S_(1) and S_(2)` have path difference of zero, and `lambda//4` respectively.

Answer

`2 :1`

Explanation

When path diff. `= 0`, phase diff. `phi_(1) = 0`
When path diff. `= lambda//4`,
phase diff. `phi_(2) = (2pi )/(4) = pi//2`
`(I_(1))/(I_(1)) = (4 I_(0) cos^(2)phi_(1)//2)/(4 I_(0) cos^(2)phi_(2)//2) = ((cos 0)^(2))/((cos pi//4)^(2)) = (2)/(1)`