Question

In Young's double slit experiment, using monochromatic light, fringes are obtained on a screen placed at some distance from the slits. If the screen is moved by $5\times {10}^{-2}m$ towards the slits, the change in the fringe width is $3\times {10}^{-5}m$. If the distance between the two slits is ${10}^{-3}m$, calculate wavelength of the light used.

Answer 1

$\Delta \beta =3\times {10}^{-5}m$
We know $\beta =\frac{D\lambda }{d}$
${\beta }^{\prime }=\frac{(D-5\times {10}^{-2}\lambda )}{d}$
$\beta ={\beta }^{\prime }=\frac{(5\times {10}^{-2}\lambda )}{d}$
$\lambda =\frac{(\beta -{\beta }^{\prime })\times d}{5\times {10}^{-2}}$
$=\frac{3\times {10}^{-5}\times {10}^{-3}}{5\times {10}^{-2}}$
$=6\times {10}^{-7}m$
$=6000\mathring{A}$