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Taking the human pupil radius as 0.25 cm, a comfortable viewing distance of 25 cm, and light of wavelength 500 nm, estimate the minimum separation between two object points that the eye can just resolve (Rayleigh criterion).

1. 30 micrometre
2. 100 micrometre
3. 300 micrometre
4. 1 micrometre

Correct answer: 30 micrometre

Solution

By the Rayleigh criterion the minimum resolvable angle is theta = 1.22*lambda/D with D the pupil diameter = 5e-3 m. theta = 1.22*500e-9/5e-3 = 1.22e-4 rad. The least separation at distance L = 0.25 m is y = theta*L = 1.22e-4*0.25 = 3.05e-5 m approx 30 micrometre.

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