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,

\[\lambda = 620 nm = 620 \times {10}^{- 9} m\]

Diameter of the convex lens,

\[d = 8 cm = 8 \times {10}^{- 2} m\]

Distance from the lens where light is to be focused,

\[D = 20 cm = 20 \times {10}^{- 2} m\]

The radius of the central bright spot is given by

\[R = 1 . 22\frac{\lambda D}{d}\]

\[     = 1 . 22 \times \frac{620 \times {10}^{- 9} \times 20 \times {10}^{- 2}}{8 \times {10}^{- 2}}\]

\[       =   1891 \times  {10}^{- 9}   m \approx 1 . 9 \times  {10}^{- 6} m\]

∴ Diameter of the central bright spot, 2R = 3.8 × 10⁻⁶ m.