A two-slit inteference, experiment uses coherent light of wavelength `5 xx 10^(-7)m`. Intensity in the interference pattern for the following points are `I_(1) , I_(2) , I_(3)`, and `I_(4)`, respectively
1. A point that is close to one slit than the other by `5 xx 10^(-7)m`.
2. A point where the light waves received from the two slits are out of phase by `(4 pi)/(3)` rad.
3. A point that is closer to one slit than the other by `7.5 xx 10^(-7) m`.
4. A point where the light waves received by the two slits are out of phase by `(pi)/(36)` rad.
Then which of following statements is/are correct?

Options

A. `I_(1) gt I_(4) gt I_(2) gt I_(3)`
B. `I_(1) gt I_(4) gt I_(2) gt I_(3)`
C. `4 I_(2) = I_(4)`
D. `I_(3) = 0`

Answer

a

Explanation

`I = I_(0) cos^(2).(xd sin theta)/(lambda)`
(1) Path difference, `delta = d sin theta = 5 xx 10^(-7) m,`
`I_(1) = I_(0) cos^(2).(pi xx 5 xx 10^(-7))/((5 xx 10^(-7) m)) = I_(0) cos^(2) (pi) = I_(0)`
(2) `I_(2) = I_(0) cos^(2) ((4pi)/(2 xx 3) "rad")`
`implies I_(0) cos^(2) ((4 pi)/(6)) = 0.25 I_(0)`
(3) `I_(3) = I_(0) cos^(2) ((pi xx 7.5 xx 10^(-7)m)/(5 xx 10^(-7)m))`
`=I_(0) cos^(2) (1.5 pi "rad") = I_(0) cos^(2) (270^(@)) = 0`
(4) `I_(4) = I_(0) cos^(2) ((pi)/(2 xx 3)) "rad" = 0.75 I_(0)`.