Question

For constructive interference between two waves of equal wavelength, the phase angle $\delta$ should be such that :

• A. $co{s}^2\frac{\delta }{2}=-1$
• B. $co{s}^2\frac{\delta }{2}=1$
• C. $co{s}^2\frac{\delta }{2}=0$
• D. $co{s}^2\frac{\delta }{2}=\infty$

Answer 1

The correct option is B $co{s}^2\frac{\delta }{2}=1$

For constructive interference between two waves of equal wavelength the path difference should be a multiple of $\lambda$ .
Let it be $n\lambda$
It path difference is $n\lambda$ then phase difference is $2n\pi$ because $\lambda$ corresponds to $2\pi$.
Thus $\delta =2n\pi$
$co{s}^2\frac{\delta }{2}=1$ in this case