A parallel beam of a monochromatic light of wavelength \( 600\ \mathrm{nm} \) passes through a long slit of width \( 0.5\ \mathrm{mm} \). The angular divergence in which most of the light is diffracted is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 2.4\times10^{-3}\ \mathrm{rad} \)
In single-slit diffraction most of the light goes into the central maximum, which lies between the first minima at \( \sin\theta = \pm\lambda/a \). Its full angular width, taken as the angular divergence, is \( 2\lambda/a \).
\( \lambda = 600\ \mathrm{nm} = 600\times10^{-9}\ \mathrm{m}, \quad a = 0.5\ \mathrm{mm} = 0.5\times10^{-3}\ \mathrm{m} \)
\( \displaystyle 2\theta = \frac{2\lambda}{a} = \frac{2 \times 600\times10^{-9}\ \mathrm{m}}{0.5\times10^{-3}\ \mathrm{m}} = 2.4\times10^{-3}\ \mathrm{rad} \)