Problem

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 (1)

I(\theta) = I_0 \cos^2 \theta

(2)

I(\theta) = \frac{I_0}{4} \cos^2 \left( \frac{\pi\theta}{8} \right)

(3)

I(\theta) = 4I_0 \cos^2 \left[ \frac{\pi}{8} (\sin \theta + 1) \right]

(4)

I(\theta) = I_0 \sin^2 \theta