Question

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

• A. K
• B. $\frac{K}{2}$
• C. $\frac{K}{4}$
• D. $\frac{K}{8}$

Answer 1

The correct option is B $\frac{K}{2}$

at zero path difference,maximum intensity $=K$ is obtained.

at path difference $\Delta x=\lambda /4$ phase difference $=\left(\delta \right)$ is :- $\delta =\frac{2\pi }{\lambda }\Delta x=\frac{2\pi }{\lambda }=\frac{\lambda }{4}=\pi /2$

thus intensity that point will be :-$K^{\prime }=K{\cos }^2\delta /2$

[assuming both sources emit light of equal intensity]

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

$=\frac{K}{2}$ (Ans)