Question

When waves of same intensity from two coherent sources reach a point with zero path different the resulting intensity is K . When the above path difference is $\lambda /4$ the intensity becomes

• A. K
• B. K/2
• C. K/4
• D. K/8

Answer 1

The correct option is C K/4

The maximum intensity is formed at $\Delta x=0$ which is $k$

Intensity at any other point having path difference $\Delta x$ is given by

$k^{\prime }=k{\cos }^2\left(\frac{\pi }{\lambda }\Delta x\right)$

For $\Delta x=\frac{\lambda }{4}$, $\frac{\pi }{\lambda }.\Delta x=\frac{\pi }{4}$ so

$k^{\prime }=k{\cos }^2\left(\frac{\pi }{4}\right)=\frac{k}{4}$