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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.
Solution
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.
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