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A converging lens of focal length 1 m and aperture diameter 5.0 cm forms the image of a star (a point source). Taking the effective wavelength for image formation as 5 × 10⁻⁵ cm and treating the lens as ideal, the diameter of the image spot is closest to:

1. zero
2. 10⁻⁶ cm
3. 10⁻⁵ cm
4. 10⁻³ cm

Correct answer: 10⁻³ cm

Solution

Diffraction limits the image to an Airy disc. The linear diameter is of order d ≈ 2.44*λ*f/D. With λ = 5×10⁻⁵ cm, f = 100 cm, D = 5 cm: d ≈ 2.44 × 5×10⁻⁵ × 100 / 5 = 2.44×10⁻³ ≈ 2.4×10⁻³ cm. To the nearest given order of magnitude this is ~10⁻³ cm.

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