Question

In a double slit experiment, the distance between the slits is 3 mm and the slits are 2 m away from the screen. Two interference patterns can be seen on the screen one due to light with wavelength 480 nm, and the other due to light with wavelength 600 nm. What is the separation on the screen between the fifth order bright fringes of the two interference patterns?

Answer 1

Separation is given by

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

where

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

$D=2m$

${\lambda }_1=480nm=480\times {10}^{-9}m$

${\lambda }_2=600nm=600\times {10}^{-9}m$

$n_1=n_2=5$

$y_2-y_1=?$

So,

$y_1=\frac{n{\lambda }_{1}D}{d}$

$y_1=\frac{5\times 480\times {10}^{-9}\times 2}{3\times {10}^{-3}}$

$y_1=1.6\times {10}^{-3}m$

Also,

$y_2=\frac{n{\lambda }_{2}D}{d}$

$y_2=\frac{5\times 600\times {10}^{-9}\times 2}{3\times {10}^{-3}}$

$y_2=2\times {10}^{-3}m$

As $y_2>y_1$

$y_2-y_1=2\times {10}^{-3}-1.6\times {10}^{-3}$

$=4\times {10}^{-}4m$

Therefore the separation on the screen between the fifth order bright fringes of the two interference patterns is $4\times {10}^{-4}m$