The image of a star (effectively a point source) is made by a convergent lens of focal length 1m and diameter of aperture 5.0 cm. If the lens is ideal and the effective wavelength in image formation is taken as 5 × 10⁻⁵ cm, the diameter of the image formed will be nearest to:
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Question

The image of a star (effectively a point source) is made by a convergent lens of focal length 1m and diameter of aperture 5.0 cm. If the lens is ideal and the effective wavelength in image formation is taken as 5 × 10⁻⁵ cm, the diameter of the image formed will be nearest to:

Options

G1 Physics · Accepted Answer

For a circular aperture, the Airy-disc diameter in the focal plane is 2.44λf/D. With λ=5×10⁻⁷ m, f=1 m and D=0.05 m, diameter≈2.44×10⁻⁵ m=2.44×10⁻³ cm, nearest 10⁻³ cm. Hence option D.