a) Given that your eye\'s visual acuity is related to the diffraction of light b

Question

a) Given that your eye's visual acuity is related to the diffraction of light by the pupil, and assuming visible light of wavelength 592 nm, what is the angle between two points that are just resolvable by an eye with a 3.05 mm diameter pupil?

b) Assume that the resolvable angle from the previous question is the limit for your eye, and that a car's headlights are spaced 1.38 m apart. From how far away could your eye just resolve the car's two headlights?

c) Assuming that the same resolvable angle from the question above is the resolution limit for your eye, what is the smallest distance between two points held at arm's length (74.0 cm) that you could just resolve?

Explanation / Answer

Part A)

Apply (angle) = (1.22)(wavelength)/D

angle = (1.22)(592 X 10-9)/(3.05 X 10-3)

angle = 2.37 X 10-4 rad (That is .0136o)

Part B)

angle = s/r

(2.37 X 10-4) = 1.38/r

r = 5830 m

Part C)

angle = s/r

(2.37 X 10-4) = s/(.74)

s = 1.75 X 10-4 m (That is .175 mm)

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