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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

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a

2.4 mm

b

2.4 cm

c

1.2 cm

d

1.2 mm

answer is D.

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Detailed Solution

$\begin{array}{l} λ = 600 nm = 6 \times 10^{- 7} m; a = 1 mm = 1 \times 10^{- 3} m \\ D = 2 mn = 1; asin θ = nλ (minima); a \frac{y}{d} = nλ \\ y = \frac{nλD}{a} = \frac{1 \times 6 \times 10^{- 7} \times 2}{1 \times 10^{- 3}} = 12 \times 10^{4} \\ width = 2 y = 24 \times 10^{- 4} = 2 .4 mm \end{array}$

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