Question

Even if the lenses of our eyes functioned perfectly, our vision would still be limited due to diffraction of light at the pupil.

Part A Using Rayleigh's criterion, what is the smallest separation between two pointlike objects that a person could clearly resolve at his near point of 23.0 cm with a pupil diameter of 2.25 mm ? Assume that the light has a wavelength of 510 nm . (To get a reasonable estimate without having to go through complicated calculations, we'll ignore the effect of the fluid in the eye.)

Express your answer in micrometers to three significant figures.

Answer 1

Given

   Rayleigh's criterion , near point d = 23 cm = 0.23m,

   pupil diameter D = 2.25 mm = 2.25*10^-3 m

   wavelength of the light is L = 510*10^-9 m

from the formula resolving power is D theta = 1.22*L/D

                   = 1.22*510*10^-9/2.25*10^-3
                   = 0.0002765333333

and now the separation is = D theta*d = 0.0002765333333*0.23 m = 0.63602666659*10^-6 m