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

In an interference arrangement similar to double-slit experiment, `S_(1)` and `S_(2)` are illuminated with coherent source microwave source each of frequeny 1 MHz
` lambda = ( c )/(f) = (3 xx 10^(8))/(10^(6)) = 300m`
`Delta x = d sin theta , phi = (2 pi)/(lambda) d sin theta = pi sin theta`
`I_(R) = 4 I cos^(2) phi // 2 = 4 I cos^(2) ((pi sin phit)/(2))`
For `I theta` to be maximum, `I_(0) = 4 I implies I = (I_0)/(4) implies I_(0) = 4 I`
`I_(R) = I_(0) cos^(2) ((pi sin theta)/(2))`
a. `theta = 0^(@) implies I_(R) I_(0)`
b. `theta = 30^(@) implies I_(R) =I_(0)/(2)`
c. `theta = 90^(@) implies I_(R) = 0`