The limit to the eye’s acuity is actually related to diffraction by the pupil. (

Question

The limit to the eye’s acuity is actually related to diffraction by the pupil.

(a)

What is the angle between two just-resolvable points of light for a 3.00-mm-diameter pupil, assuming an average wavelength of 576 nm?

___________rad ( ± 1E-6 rad)

(b)

Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are 1.30 m apart?

_______________km ( ± 0.01 km)

(c)

What is the distance between two just-resolvable points held at an arm’s length (0.800 m) from your eye?

____________ mm ( ± 0.001 mm)

Explanation / Answer

a) The angle is calculated as,

theta = 1.22* lambda/D = 1.22*576x10-9 /3x10-3 = 2.34x10-4 rad

b)

The distance is calculated as,

L = y/theta = 1.3/(2.34x10-4 rad)= 5.55x103 m = 5.55 km

c)

The required distance is,

y = L*theta = 0.800*2.34x10-4 = 0.187 mm

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