Question

Two identical light waves having phase difference ${}^{\prime }{\varphi }^{\prime }$ propagate in same direction. When they superpose, the intensity of 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)

${\cos }^2\frac{\varphi }{2}$

The resultant intensity of two identical light waves having phase difference $\varphi$ propagate in same direction is

$I_r=I+I+2Icos\varphi =4Ico{s}^2\left(\frac{\varphi }{2}\right)$

Hence the resultant intensity of the wave is directly proportional to $co{s}^2\frac{\varphi }{2}$