Question

A long narrow horizontal slit is paced 1 mm above a horizontal plane mirror. The interference between the light coming directly from the slit and that after reflection is seen on a screen 1⋅0 m away from the slit. Find the fringe-width if the light used has a wavelength of 700 nm.

Answer 1

Given:
Separation between two slits, $d\text{'}=2d=2\mathrm{mm}=2\times {10}^{-3}\mathrm{m}$ (as d = 1 mm)
Wavelength of the light used, $\lambda =700\mathrm{nm}=700\times {10}^{-3}\mathrm{m}$
Distance between the screen and slit (D) = 1.0 m
It is a case of Lloyd's mirror experiment.
$$\begin{gathered} \mathrm{Fringe}\mathrm{width},\beta =\frac{\mathrm{\lambda D}}{d\text{'}} \\ =\frac{700\times {10}^{-9}\times 1}{2\times {10}^{-3}} \\ =0.35\times {10}^{-3}\mathrm{m}=0.35\mathrm{mm} \end{gathered}$$

Hence, the width of the fringe is 0.35 mm.