Question

In Young's double slit experiment, the slits are separated by $0.28mm$ and the screen is placed at a distance of $1.4m$ away from the slits. The distance between the central bright fringe and the fifth dark fringe is measured to be $1.35cm$. Calculate the wavelength of the light used. Also find the fringe width if the screen is moved $0.4m$ towards the slits, for the same experimental setup.

Answer 1

$d=0.28mm=0.28\times {10}^{-3}m$

$D=1.4m$

$x_n=1.35cm=1.35\times {10}^{-2}m$

$n=5$

For $n^{th}$ dark fringe,
$x_n=\frac{(2n-1)}{2}\frac{\lambda D}{d}$

$1.35\times {10}^{-2}=\frac{[(2\times 5)-1]}{2}\times \frac{\lambda \times 1.4}{0.28\times {10}^{-3}}$

$\lambda =\frac{1.35\times {10}^{-2}\times 0.28\times {10}^{-3}\times 2}{1.4\times [(2\times 5)-1]}=0.06\times {10}^{-5}=6000A$

When $D=1.4-0.4m=1m$

$\beta =\frac{\lambda D}{d}=\frac{6000\times {10}^{-10}\times 1}{0.28\times {10}^{-3}}=21428.5714\times {10}^{-7}=0.21cm=2.1429mm$