In this problem, you will determine the finest detail that the human eye can dis

Question

In this problem, you will determine the finest detail that the human eye can discern at a set distance. Assume a pinhole camera model where the distance between the pinhole and the retina along the visual axis is 17mm. Assume that the density of cones in the fovea is 150,000 elements per mm2 and that the cones are arranged in a grid with no spacing between them.

Suppose you are looking at a scene with alternating black and white lines of equal width. Assume that you are able to discern the individual lines up to the point where the image of a line on your retina is smaller than a single cone. That is, when the image of a line is smaller than a cone, you can no longer tell it apart from an adjacent line.

Calculate the width of the smallest line you can discern when the scene is:

a) 0.2 meters from your eye (from the pinhole). (Note, due some simplifying assumptions, you will probably get a result which seems smaller than you expect.)

b) 100 meters from your eye.

Explanation / Answer

disregarding diffraction
a. distance of fovea from the aperture of eye d = 17 mm
   distance of the object from the eye, D = 0.2 m
   so width of the smallest line on the retina, w = ?
   w^2 = 1/150,000
   w = 0.002581 mm
   so width of the smallest line in scene that can be seen W = ?
   from ratio proportion
   W/D = w/d
   W = w(D/d) = 0.002581*(0.2/17*10^-3) = 0.03037 m
b. similiarly to previous question
   W = 0.002581*(100/17*10^-3) = 15.1881 m

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