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 on the retina. In order 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 (um) is typical near the center of the eye. We shall model the eye as a sphere 2.50cm in diameter with a single thin lens at the front and the retina at the rear, with light receptor cells 5.00 microns in diameter. a)What is the smallest object you can resolve at a near point of 25.0cm ? b)What angle is subtended by this object at the eye? Express your answer in units of minutes (1degree = 60 minutes) (Note: There are other limitations, such as the bending of light as it passes through the pupil, but we shall ignore them here.)

Explanation / Answer

a) here image height,h' = 5 micron = 5*10^-4 cm
image distance,v = 2.5 cm
object distance,u = -25 cm (- sign due to sign convention)
since for lenses,magnification, m = -v/u = -2.5/-25 = 0.1 = h'/h (h is object height)
0.1 = 5*10^-4/h => h = 0.005 cm = 0.05 mm = smallest object dimension Ans

b)the angle subtended by object at eye is given by formula

= 2tan-1(h/2u) => = 2tan-1(5*10^-5/2*0.25) = 0.01146 degrees = 0.68755 minutes Ans

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