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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?

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Solution

Given: Wavelength of the light used, $\mathrm{\lambda }=620\mathrm{nm}=620×{10}^{-9}\mathrm{m}\phantom{\rule{0ex}{0ex}}$ Diameter of the convex lens, $d=8\mathrm{cm}=8×{10}^{-2}\mathrm{m}$ Distance from the lens where light is to be focused, $D=20\mathrm{cm}=20×{10}^{-2}\mathrm{m}$ The radius of the central bright spot is given by $R=1.22\frac{\lambda D}{d}\phantom{\rule{0ex}{0ex}}=1.22×\frac{620×{10}^{-9}×20×{10}^{-2}}{8×{10}^{-2}}\phantom{\rule{0ex}{0ex}}=1891×{10}^{-9}\mathrm{m}\approx 1.9×{10}^{-6}\mathrm{m}$ ∴ Diameter of the central bright spot, 2R = 3.8 × 10−6 m.

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