Two identical sources each of intensity `I_(0)` have a separation `d = lambda // 8`, where `lambda` is the wavelength of the waves emitted by either source. The phase difference of the sources is `pi // 4` The intensity distribution `I(theta)` in the radiation field as a function of `theta` Which specifies the direction from the sources to the distant observation point P is given by

Options

A. `I (theta) = I_(0) cos^(2) theta`
B. `I (theta) = (I_(0))/(4) cos^(2) ((pi theta)/(8))`
C. `I (theta) = 4 I_(0) cos^(2) [(pi)/(8) (sin theta + 1)]`
D. `I (theta) = I_(0) sin^(2) theta`

Answer

c

Explanation

`Delta x = sin theta = (lambda)/(8) sin theta`
`Delta phi =` phase difference at P
`Delta phi = (2 pi)/(lambda) (Delta x) + Delta phi' = (2 pi)/(lambda) ((lambda)/(8) sin theta ) + (pi)/(4)`
`I (theta) = 4 I_(0) cos^(2) ((Delta phi)/(2))`
`= 4 I_(0) cos^(2) [(pi)/(8) (1 + sin theta)]`