A person\'s eye has a pupil diameter of .2 cm and has a length of about 2.5 cm (

Question

A person's eye has a pupil diameter of .2 cm and has a length of about 2.5 cm (from lens to retina). If light of 550 nm is used, find the following:

a) minimum distance between resolved images on the retina of the eye, ignoring any lens aberration

b) the distance apart that two point sources of light can have at the near point of the eye (N=25 cm) and just be resolved

c) what microscope magnification would be needed for the eye to just clearly image these two point sources of light if they are only 500 nm apart

d) with a 10X eyepiece and a tube length of 17.0 cm, find the objective focal length needed to achieve the magnification in part c

Explanation / Answer

The diamter of the eye D = 0.2cm The length from lens to retina L = 2.5cm the wavelength of light = 550nm (a) the minimum distance between resolved images                    s = L = L(1.22/D)                        = (2.5*10^-2)(1.22*550*10^-9)/0.2*10^-2)                        = 8.387*10^-6 m or 8.4m (b) the minimum distance between resolved images at L = 25cm                   s = L = L(1.22/D)                        = (25*10^-2)(1.22*550*10^-9)/0.2*10^-2)                        = 83.87*10^-6 m or 84m (c) The magnification                        M = 8.4*10^-6/500*10^-9 = 16.8 (d) The magnification of the compound microscope         M = mme         16.8    = (17/f)10 therefore the focal length        f = 16.8/1.7 = 9.88cm             s = L = L(1.22/D)                        = (25*10^-2)(1.22*550*10^-9)/0.2*10^-2)                        = 83.87*10^-6 m or 84m (c) The magnification                        M = 8.4*10^-6/500*10^-9 = 16.8 (d) The magnification of the compound microscope         M = mme         16.8    = (17/f)10 therefore the focal length        f = 16.8/1.7 = 9.88cm

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