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

Answer 1

Answer: (B)

The resultant intensity after the interference of the two light waves is
$I_R=I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi$
For two identical light waves, $I=I_1=I_2$
Therefore,
$I_R=I+I+2\sqrt{I^2}\cos \varphi =2I1+\cos \varphi$
$\Rightarrow I_R=4I{\cos }^2\frac{\varphi }{2}$
$\therefore I_R\propto {\cos }^2\frac{\varphi }{2}$