Physics - Wave Optics Question with Solution | TestHub

For destructive interference (dark fringes) in Young's double slit experiment, the path difference $\Delta x$ is an odd multiple of $\frac{\lambda }{2}$.

For the $n^{\text{th}}$ dark fringe, where $n=1,2,3,\dots$, the path difference is given by:

$\Delta x=(2n-1)\frac{\lambda }{2}$

The phase difference $\Delta \varphi$ is related to the path difference by:

$\Delta \varphi =\frac{2\pi }{\lambda }\Delta x$

Substituting the value of $\Delta x$:

$\Delta \varphi =\frac{2\pi }{\lambda }\times (2n-1)\frac{\lambda }{2}$

$\Delta \varphi =(2n-1)\pi$

Answer: $(2n-1)\pi$