A parallel beam of monochromatic light of wavelength 900 nm passes through a long slit of width 0.4 mm. The angular divergence in which most of the light is diffracted, is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 4.5 \times 10^{-3}\,\mathrm{rad} \)
In single-slit diffraction most of the light goes into the central maximum, which lies between the first minima on either side, at \( \sin\theta = \pm\lambda/a \). Its angular width is therefore
\( \displaystyle 2\theta = \frac{2\lambda}{a} \)
\( \lambda = 900\,\mathrm{nm} = 9\times10^{-7}\,\mathrm{m} \)
\( a = 0.4\,\mathrm{mm} = 4\times10^{-4}\,\mathrm{m} \)
\( \displaystyle 2\theta = \frac{2 \times 9\times10^{-7}}{4\times10^{-4}} = 4.5\times10^{-3}\,\mathrm{rad} \)