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.

Options

A. `3:2`
B. `2:1`
C. `sqrt(2):1`
D. `4:1`

Answer

B

Explanation

Let `I_(0)` is intensity of light emitted from the source, then resultant intensity `I=4I_(0)"cos"^(2)(phi)/(2)`
`I_(1)=4I_(0)"cos"^(2)(phi)/(2)=4I_(0)`
Now, path difference `Delta x=(lambda)/(4)`
Phase difference `phi=(2pi)/(lambda)xx Delta x=(2pi)/(lambda)xx(lambda)/(4)=(pi)/(4)`
`and I_(2)=4I_(0)"cos"^(2)(pi)/(4)=2I_(0)`
`I_(1):I_(2)=2:1`