In an interference arrangement similar to Young's double-slit experiment, the slits S_1 and S_2 are illuminated with coherent microwave sources, each of frequency 10^6 Hz. The sources are synchronized to have zero phase difference. The slits are separated by a distance d=150.0 m. The intensity I (theta) is measured as a function of theta, where theta is defined as shown. If I_0 is the maximum intensity, then I (theta) for 0lethetale90degree is given by

Options

A. `I (theta) = I_(0)//2` for `theta = 30^(@)`
B. `I (theta) = I_(0)//4` for `theta = 90^(@)`
C. `I (theta) = I_(0)` for `theta = 0^(@)`
D. `I (theta)` is constant for all value of `theta`

Answer

c

Explanation

We know that
`I = I_(0) cos^(2) ((delta)/(2))`
where
`delta = (2pi)/(lambda) xx (D y)/(d) = (2pi tan theta)/(lambda)`
`I = I_(0) cos^(2) ((pi d tan theta)/(lambda))`
`= I_(0) cos^(2) ((pi xx 150 xx tan theta)/(3 xx 10^(8)//10^(6)))`
`= I_(0) cos^(2) ((pi)/(2) tan theta)`
For `theta = 30^(@), I = I_(0) cos^(2) 52`
For `theta = 90^(@), I = I_(0) cos^(2) pi//2 = 0`
Hence, (c) is the correct option.