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You are in an airplane at an altitude of 10,000 m. The diameter of the pupil of your eye is about 3.0 mm and the wavelength of light is 550 nm. What is the minimum separation between two objects on the ground that you can resolve?

1. 1.24 m
2. 2.24 m
3. 9.92 m
4. 4.48 m

Correct answer: 2.24 m

Solution

Rayleigh criterion for angular resolution: theta_min = 1.22 * lambda / d, where d is aperture diameter. theta_min = 1.22 * 550e-9 m / 3e-3 m = 1.22 * 1.833e-4 = 2.237e-4 rad. Minimum separation = theta_min * altitude = 2.237e-4 * 10000 = 2.237 m ≈ 2.24 m.

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