Find the focal length of the lens used to focus an image of distant object on focal plane of the lens if the radius of central bright dot is `5 mum`, when it illuminated by ray of wavelength 400 nm and the radius of the circular aperture is 2.5 cm.

Explanation

To find the focal length of the lens used to focus an image of a distant object on the focal plane of the lens, we can use the formula for the radius of the central bright dot in diffraction patterns:

\[ r_0 = \frac{0.61 \lambda f}{A} \]

where:
- \( r_0 \) is the radius of the central bright dot,
- \( \lambda \) is the wavelength of the light,
- \( f \) is the focal length of the lens,
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