A beam of light of from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is [2014]

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Solution

Q.
A beam of light of $λ = 600$ $nm$ from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between first dark fringes on either side of the central bright fringe is [2014]

1 1.2 cm

2 1.2 mm

3 2.4 cm

4 2.4 mm

Ans.
(4)

Here, $λ = 600$ $nm = 600 \times 10^{- 9}$ $m$

$a = 1$ $mm = 10^{- 3}$ $m, D = 2$ $m$

Distance between the first dark fringes on either side of the central bright fringe is also the width of central maximum.

$Width of central maximum = \frac{2 λ D}{a}$

$= \frac{2 \times 600 \times 10^{- 9} m \times 2 m}{10^{- 3} m} = 24 \times 10^{- 4} m = 2.4 \times 10^{- 3} m = 2.4$ $mm$

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