Question

Light of wavelength 560 nm goes through a pinhole of diameter 0.20 mm and falls on a wall at a distance of 2.00 m. What will be the radius of the central bright spot formed on the wall?

Answer 1

Given:
Wavelength of the light used, $\mathrm{\lambda }=560\mathrm{nm}=560\times {10}^{-9}\mathrm{m}$
Diameter of the pinhole, d = 0.20 mm = 2 × 10⁻⁴ m
Distance of the wall, D = 2m
We know that the radius of the central bright spot is given by
$$\begin{gathered} R=1.22\frac{\lambda D}{d} \\ =1.22\times \frac{560\times {10}^{-9}\times 2}{2\times {10}^{-4}} \\ =6.832\times {10}^{-3}\mathrm{m}\mathrm{or}=0.683\mathrm{cm} \end{gathered}$$

Hence, the diameter 2R of the central bright spot on the wall is 1.37 cm.