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Question

Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can resolve at 500 nm wavelength is


Solution

Assuming human pupil to have a radius r = 0.25 cm or diameter d = 2r = 0.5 cm
The wavelength of light is λ = 500 nm = 5 × 107 m.
sin θ=1.22λd
sin θ1.22×5×1070.5×102 = 1.22 × 104
The distance of comfortable viewing is D = 25 cm = 0.25 m.
Let x be the minimum separation between two objects that the human eye can resolve.
sin θxD
sin θ = 0.25 × 1.22 × 104 = 3 × 105 m = 30 μm.

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