The limit to the eye’s acuity is actually related to diffraction by the pupil. (
ID: 1371798 • Letter: T
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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