Question

in Young's double slit experiment, the slits are $2mm$ apart and are illuminated with a mixture of two wavelength $\lambda =7500\mathring{A}$ and ${\lambda }^{\prime }=9000\mathring{A}$. At what minimum distance from the common central bright fringe on a screen $2m$ from the slits will a bright fringe from one interference pattern coincide with the bright fringe from the other?

Answer 1

Given

$\lambda =7500\mathring{A}$

${\lambda }^{\prime }=9000\mathring{A}$

$D=2cm$

$d=2mm=2\times {10}^{-3}$

We have

$\frac{\lambda }{{\lambda }^{\prime }}=\frac{h_1}{h_2}$

$=\frac{7500}{9000}=\frac{5}{6}$

As,

$x=\frac{u^{\prime }{\lambda }^{\prime }D}{d}$

$x=\frac{5\times 9000\times {10}^{-10}\times 2}{2\times {10}^{-3}}$

$=9mm$