A parallel beam of monochromatic light of wavelength 460 nm passes through a long slit of width 0.1 mm. What is the angular divergence in which most of the light is diffracted?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 9.2 \times 10^{-3}\,\mathrm{rad} \)
In single-slit diffraction most of the light goes into the central maximum, which lies between the first minima on either side. The first minima are at \( \theta = \pm\lambda/a \), so the angular spread of the central maximum is
\( \displaystyle 2\theta = \frac{2\lambda}{a} \)
\( \lambda = 460\,\mathrm{nm} = 4.6\times10^{-7}\,\mathrm{m} \)
\( a = 0.1\,\mathrm{mm} = 1\times10^{-4}\,\mathrm{m} \)
\( \displaystyle 2\theta = \frac{2 \times 4.6\times10^{-7}}{1\times10^{-4}} = 9.2\times10^{-3}\,\mathrm{rad} \)