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 7.75 mm diameter pupil, assuming the average wavelength of 524 nm? 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 1.60 m apart? What is the distance between two just-resolvable points held at an arm's length (0.800 m) from your eye?

Explanation / Answer

Given

   diameter of the pupil is D =7.75 mm

   wavelength of light is Lambda L = 524 nm

we know that the minimum diffraction angle is theta = 1.22 *L /D

  
           theta = 1.22*524*10^-9/(7.75*10^-3)
  
           Theta = 8.2488*10^-5 rad

so the angle is 8.2488*10^-5 rad

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and from the relation S = r*theta

           r = s/theta
           r = 1.6/8.2488*10^-5 m

           r = 19396.760 m

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       r = 0.8/8.2488*10^-5 m = 0.0969838037048 *10^5 m = 9.7 km

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