Question

Phase difference $\left(\varphi \right)$ and path difference $\left(\delta \right)$ are related by :

• A. $\frac{2\pi }{\lambda }\delta$
• B. $\frac{\pi }{2\lambda }\delta$
• C. $\frac{\lambda }{2\pi }\delta$
• D. $\frac{2\lambda }{\pi }\delta$

Answer 1

The correct option is A $\frac{2\pi }{\lambda }\delta$

Relation between phase difference and path difference is
$\varphi =\frac{2\pi }{\lambda }\delta$
where $\lambda$ is the wavelength of the wave.
For constructive interference :
Path difference $\delta =n\lambda$ $⟹\varphi =2n\pi$
where $n=0,1,2,...$
For destructive interference :
Path difference $\delta =(n+\frac{1}{2})\lambda$ $⟹\varphi =(2n+1)\pi$