Question

Green light of wavelengths $100\mathring{A}$, from a narrow slit is incident on a double slit. If the overall separation of $10$ fringes, on a screen $200cm$ away, is $2cm$, find the slit separation.

• A. ${10}^{-5}m$
• B. ${10}^{-7}m$
• C. ${10}^{-6}m$
• D. ${10}^{-8}m$

Answer 1

The correct option is A ${10}^{-5}m$

Given,

$\lambda =100A^{\circ }=100\times {10}^{-10}m$

separation between slit and screen(D) is $200cm=2m$

Separation of 10 fringes is $2cm$ That means,

$10\beta =2cm=2\times {10}^{-2}m\beta =\frac{2\times {10}^{-2}}{10}=0.2\times {10}^{-2}m$

And we know that in double slit separation fringe width$\beta$ is

$\beta =\frac{\lambda D}{d}d=\frac{\lambda D}{\beta }$

Substitute all value in above equation

$d=\frac{100\times {10}^{-10}\times 2}{0.2\times {10}^{-2}}={10}^{-5}m$

Correct option is A.