Question

Two slits separated by a distance of $1mm$ are illuminated by light of wavelength $6.5\times {10}^{-7}m$. Interference fringes are oberved on a screen placed at a distance of $1$ from the slits. Calculate the distance between the third dark fringe and fifth bright fringe.

Answer 1

Given:

Slit separation, $d=1mm=1\times {10}^{-3}m$

Wavelength, $\lambda =6.5\times {10}^{-7}m$

Screen distance , $D=1m$

To find:

Distance between 3${}^{rd}$ dark fringe and 5${}^{th}$ bright fringe

We know,

For distance of dark fringe, $y_n=\frac{(2n-1)\lambda D}{2d}$

And, for distance of bright fringe, $y_n=\frac{n\lambda D}{d}$

$y_5-y_3=\frac{5\times 6.5\times {10}^{-7}\times 1}{{10}^{-3}}-\frac{(2\times 3-1)\times 6.5\times {10}^{-7}\times 1}{2\times {10}^{-3}}=32.5\times {10}^{-4}-16.25\times {10}^{-4}=16.25\times {10}^{-4}m$

Hence the distance between the third dark fringe and fifth bright fringe is 1.625mm