Question

A parallel beam of monochromatic light of wavelength 450nm passes through a slit of width 0.2 mm. The angular divergence is?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{Most}\mathrm{of}\mathrm{the}\mathrm{light}\mathrm{is}\mathrm{diffracted}\mathrm{between}\mathrm{the}\mathrm{two}\mathrm{first}\mathrm{order}\mathrm{minima}.\mathrm{These}\mathrm{minima}\mathrm{occur}\mathrm{at}\mathrm{angles}\mathrm{given}\mathrm{by} \\ \mathrm{a}\mathrm{sin\theta }=\pm \mathrm{\lambda } \\ \mathrm{sin\theta }\approx \mathrm{\theta }=\frac{\pm \mathrm{\lambda }}{\mathrm{a}} \\ \mathrm{\theta }=\frac{450\times {10}^{-9}}{0.2\times {10}^{-3}} \\ \mathrm{\theta }=2.25\times {10}^{-3}\mathrm{rad} \\ \mathrm{Angular}\mathrm{divergence}=2\mathrm{\theta } \\ \mathrm{Angular}\mathrm{divergence}=2\times 2.25\times {10}^{-3} \\ \mathrm{Angular}\mathrm{divergence}=4.5\times {10}^{-3}\mathrm{rad} \end{gathered}$$