The smallest object we can resolve with our eye is limited by the size of the li

Question

The smallest object we can resolve with our eye is limited by the size of the light receptor cells in the retina. In order for us to distinguish any detail in an object, its image cannot be any smaller than a single retinal cell. Although the size depends on the type of cell (rod or cone), a diameter of a few microns is typical near the center of the eye. We shall model the eye as a sphere 2.50 cm in diameter with a single thin lens at the front and the retina at the rear, with light receptor cells in diameter. (a) What is the smallest object you can resolve at a near point of 25 cm? (b) What angle is subtended by this object at the eye? Express your answer in units of minutes and compare it with the typical experimental value of about 1.0 min. (Note: There are other limitations, such as the bending of light as it passes through the pupil, but we

Explanation / Answer

The dia of light receptor cells must be 5 microns....not mm So, R = 2.5 cm f = 1.25 cm v = 2.5 cm dia of light receptop cell = max ht of image = hi = 5 * 10^-6 m u = -25 cm So, M = v / u = -0.1 hi / ho = -0.1 ho = 5 * 10^-6 m = 50 microns b) angle subtended = 0.11459 degree = 0.687 min

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