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 = 45^(@)`
B. `I(theta) = I_(0)//4 fortheta = 90^(@)`
C. `I (theta) = I_(0) for theta = 0^(@)`
D. `I(theta)` is constant for all values of `theta`

Answer

C

Explanation

The intensity of light is `I(theta) = I_(0) cos^(@) ((delta)/(2))`
where `delta = (2pi)/(lambda) (Delta x) = ((2pi)/(lambda)) (d sin q)`
(i) For `theta = 30^(@)`
`lambda = (c )/(v) = (3xx10^(8))/(10^(6)) = 300 and d = 150 m`
`delta = ((2pi)/(300)) (150) ((1)/(2)) = (pi)/(2) (delta)/(2) = (pi)/(4)`
`I(theta) = I_(0) cos^(2) ((pi)/(4)) = (I_(0))/(2)` (option a)
(ii) For `0 = 90^(@) d = ((2pi)/(300)) (150) (1) = p`
or `(delta)/(2) = (pi)/(2) and I (theta) = 0`
(iii) For `theta = 0^(@), d = 0 or (delta)/(2) = 0`
`I(theta) = I_(0)` (option c)