Question

Two identical light waves having phase differenceϕ propagate in the same direction. When they superpose, the intensity of the resultant wave is proportional to

• A. $\cos ^2 \phi$
• B. $\cos ^2 \frac{\phi}{2}$
• C. $\cos ^2 \frac{\phi}{3}$
• D. $\cos ^2 \frac{\phi}{4}$

Answer 1

Answer: (B)

The resultant intensity after the interference of the two light waves is
$I_R=I_1+I_2+2 \sqrt{I_1 I_2} \cos \phi$
For two identical light waves, $I=I_1=I_2$
Therefore,
$I_R=I+I+2 \sqrt{I^2} \cos \phi=2 I 1+\cos \phi $
$\Rightarrow I_R=4 I \cos ^2 \frac{\phi}{2}$
$\therefore I_R \propto \cos ^2 \frac{\phi}{2}$