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, \[d' = 2d = 2 mm = 2 \times {10}^{- 3} m..........\left(\text{as d = 1 mm}\right)\]

Wavelength of the light used,

\[\lambda = 700  nm = 700 \times  {10}^{- 3}   m\]

Distance between the screen and slit (D) = 1.0 m

It is a case of Lloyd's mirror experiment.

\[\text{Fringe width, }\beta = \frac{\lambda D}{d'}\]

\[ = \frac{700 \times {10}^{- 9} \times 1}{2 \times {10}^{- 3}}\]

\[ = 0 . 35 \times {10}^{- 3} m = 0 . 35\text{ mm}\]

Hence, the width of the fringe is 0.35 mm.