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A narrow slit of width 2 mm is illuminated by the light of wavelength $5000 \overset{\circ}{A}$ . What is the distance between the first dark fringe on either side on a screen at a distance of 1 m is

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0.5 mm

1 mm

5 mm

10 mm

answer is B.

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Detailed Solution

$\begin{array}{l} Here, a = 2 mm = 2 \times 10^{- 3} m \\ λ = 500 nm = 500 \times 10^{- 9} m = 5 \\ \times 10^{- 7} m, D = 1 m \end{array}$

The distance between the first minima on either side on

$\begin{array}{l} A screen = \frac{2 λD}{a} = \frac{2 \times 5 \times 10^{- 7} \times 1}{2 \times 10^{- 3}} \\ = 5 \times 10^{- 4} m = 0 .5 \times 10^{- 3} m \\ = 0 .5 mm \end{array}$

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