Question

A convex lens of diameter 8.0 cm is used to focus a parallel beam of light of wavelength 620 nm. If the light is focused at a distance of 20 cm from the lens, what would be the radius of the central bright spot formed?

Answer 1

Given:
Wavelength of the light used, $\mathrm{\lambda }=620\mathrm{nm}=620\times {10}^{-9}\mathrm{m}$
Diameter of the convex lens, $d=8\mathrm{cm}=8\times {10}^{-2}\mathrm{m}$
Distance from the lens where light is to be focused, $D=20\mathrm{cm}=20\times {10}^{-2}\mathrm{m}$
The radius of the central bright spot is given by
$$\begin{gathered} R=1.22\frac{\lambda D}{d} \\ =1.22\times \frac{620\times {10}^{-9}\times 20\times {10}^{-2}}{8\times {10}^{-2}} \\ =1891\times {10}^{-9}\mathrm{m}\approx 1.9\times {10}^{-6}\mathrm{m} \end{gathered}$$
∴ Diameter of the central bright spot, 2R = 3.8 × 10⁻⁶ m.