Consider an interference arrangement similar to YDSE. Slits `S_(1)` and `S_(2)` are illuminated with coherent microwave sources each of frequency 2 MHz The sources are synchronized to have zero phase difference. The slits are separated by distance d= 75m. The intensity `I_((theta))` is measured as a function of `theta` where `theta` is defined as shown in figure. if `I_(0)` is maximum intensity then calculated `I_((theta))` for `(i) theta= 0^(@), (ii) theta=pi//6 and (iii) theta = pi//2`

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`