Question

Derive an expression for bandwidth of interference fringes in Young's double slit experiment.

Answer 1

Fringe width $Y$ is defined as the distance between two consecutive dark fringe or distance between to consecutive bright fringe.

$X_n=\frac{n\lambda D}{d}$

$Y=X_n-X_{n-1}$

$=\frac{n\lambda D}{d}-\frac{(n-1)\lambda D}{d}$

$y=\frac{\lambda D}{d}$