Using light from a monochromatic source to study diffraction in a single slit of width 0.1 mm, the line width of central maxima is measured to be 5 mm on a screen held 50 cm away. The wavelength of light used is _______.

Fill in the blank with the correct answer from the options given below.

$5 \times 10^{-7} m$

For central bright fringe approximately the width is $ y = \frac{\lambda D}{a} $

$\Rightarrow 5 \times 10^{-3} = \frac{2\lambda \times 0.5}{0.1\times 10^{-3}$

$ \lambda = 2\times 10^{-7} m$

The correct answer is Option (3) → $5 \times 10^{-7} m$