At two points P and Q on a screen in Young's double slit experiment, waves from slits `S_(1) and S_(2)` have a path difference of O and `(lambda)/(4)` respectively. The ratio of intensities at P and Q will be ......

Options

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

Answer

B

Explanation

`I_(P)=I_(0)"cos"^(2){(k(r_(2)-r_(1)))/(2)}`
`=I_(0)cos^(2){K((0)/(2))} " " [ :. r_(2)-r_(1)=0]`
`=I_(0)cos^(2)(0)`
`I_(P)=I_(0) " "…(1)`
`I_(Q)=I_(0)cos^(2){(k(r_(2)-r_(1)))/(2)}`
`=I_(0)cos^(2){(2pi)/(lambda)xx(lambda)/(8)} " " [:.r_(2)-r_(1)=(lambda)/(4)]`
`=I_(0)cos^(2){(pi)/(4)}`
`=I_(0)((1)/(sqrt(2)))^(2)`
`I_(Q)=(I_(0))/(2) " "....(2)`
`:.(I_(p))/(I_(Q))=(I_(0))/(I_(0)/(2))=(2)/(1)`
`:.I_(p)=I_(Q)=2:1`