30. A beam of light of λ = 600 nm from a dis- tant 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:

30. 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:

(a) 1.2 cm

(b) 1.2 mm

(c) 2.4 cm

(d) 2.4 mm

Answer :  (d) 2.4 mm

\( 2\beta = 2 \cdot \frac{\lambda D}{d}\)

\(= 2 \cdot \frac{600 \times 10^{-9} \times 2}{1 \times 10^{-3}}\)

\(= 24 \times 10^{-4} = 2.4 \text{ mm}\)