A beam of light of wavelength 500 nm from a distant source falls on a single slit $10^{-4} m$ wide and the resulting diffraction pattern is observed on a screen 2 m away. The width of the central bright fringe is

$2 × 10^{-2} m$

The correct answer is Option (4) → $2 × 10^{-2} m$

Wavelength of light: $\lambda = 500 \,\text{nm} = 500 \times 10^{-9}\,\text{m}$

Slit width: $a = 10^{-4}\,\text{m}$

Distance to screen: $D = 2\,\text{m}$

Width of central maximum: $\Delta y = \frac{2 \lambda D}{a}$

$\Delta y = \frac{2 \times 500 \times 10^{-9} \times 2}{10^{-4}}$

$\Delta y = \frac{2000 \times 10^{-9}}{10^{-4}}$

$\Delta y = 2000 \times 10^{-5}$

$\Delta y = 2 \times 10^{-2}\,\text{m} = 2\,\text{cm}$

Answer: The width of the central bright fringe is 2 cm.