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. What is the angle between two just-resolvable points of light for a 6.75 mm diameter pupil, assuming the average wavelength of 539 nm? degree 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 1.40 m apart? m What is the distance between two just-resolvable points held at an arm's length (0.700 m) from your eye? m

Explanation / Answer

1) Using Rayleigh criterion

sin theta = 1.22 lambda/D

theta = arcsin(1.22*539E-9/6.75E-3)=0.00558 degrees

2) Now

tan theta = y/L

L = 1.4/tan(0.00558 degrees)=14370.9 m

3) Now

y = L tan theta = 0.7*tan(0.00558 degrees)= 6.82E-5 m

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