Leaving Certificate Physics Practice Test

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Using the Rayleigh criterion, estimate the angular resolution for light with wavelength 550 nm observed through an aperture of diameter 2.0 cm.

3.36×10^-5 rad 1.22×10^-4 rad 6.9×10^-5 rad 2.7×10^-6 rad

Correct Answer:

3.36×10^-5 rad

Explanation:

The Rayleigh criterion says the smallest resolvable angle for a circular aperture is θ ≈ 1.22 λ / D. Using λ = 550 nm = 5.50 × 10^-7 m and D = 2.0 cm = 0.02 m, the ratio λ/D is 5.50e-7 / 0.02 = 2.75 × 10^-5. Multiplying by 1.22 gives θ ≈ 3.36 × 10^-5 rad. This is the estimated angular resolution. In arcseconds, that’s about 6.9″, illustrating how a modest aperture limits the detail you can resolve with visible light.

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