Question

A beam of light of wavelength $600\, nm$ 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 the 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 1

Answer: (D)

2.4 mm

Answer 2

$\beta=\frac{\lambda D}{d}=\frac{600 \times 10^{-9} \times 2}{1 \times 10^{-3}}$ $=12 \times 10^{-4} m$ So, distance between the first dark fringes on either side of the central bright fringe $X =2 \beta$ $=2 \times 12 \times 10^{-4} m$ $=24 \times 10^{-4} m$ $=2.4\,mm$