In an interference arrangement similar to double-slit experiment, `S_(1)` and `S_(2)` are illuminated with coherent source microwave source each of frequency 1 MHz. the sources are synchronized to have zero phase difference . This slits are separated by distance `d = 150.0m` The intensity `I (theta)` is measured as a funciton of `theta`, where `theta` is defined as shown in figure. If `I_(0)` is maximum intensity, calculate `I (theta)`
For :
a. `theta = 0` b. `theta = 30^(@)`
c. `theta = 90^(@)`

Explanation

`upsilon=1 MHz=10^(6) Hz, d=150 m`
`c=upsilonlambda implies lambda=c/v =(3xx10^(8))/10^(6)=300 m`
`Deltax=d sin theta`
`phi=(2pi)/lambda Deltax=(2pi)/lambda d sin theta=(2pi)/300xx150 sin theta =pi sin theta`
`I_(R)=I_(0) cos^(2)(phi//2)=I_(0) cos^(2) ((pi sin theta)/2)`
(a) `theta=0, I_(R)=I_(0)`
(b) `theta=30^(@), I_(R)=I_(0) cos^(2)((pi sin 30^(@))/2)=I_(0) cos^(2) (pi//4)=I_(0)/2`
(c ) `theta=90^(@), I_(R)=0`