Question

Constants Part A The maximum resolution of the eye depends on the diameter of the opening of the pupil (a diffraction effect) and the size of the light receptor cells (rods or cones) on the retina. The size of the retinal cells (about 5.0 am in diameter) limits the size of an object at the near point (25 em )of the eye to a height of about 50 pam. (To get a reasonable estimate without having to go through complicated calculations, we shall ignore the effect of the fluid in the eye.) Given that the diameter of the human pupil is about 2.0 mm does the Rayleigh criterion allow us to resolve a 50 μm-tall object at 25 cm from the eye with light of wavelength 560 nm ? Yes O No. Submit Request Answer Part B According to the Rayleigh criterion, what is the shortest object we could resolve at the 25 cm near point with light of wavelength 560 nm? Express your answer in micrometers to two significant figures , 8.54.10 з

Answer 1

"(A) theta = 50 mu m/25 cm = 2 times 10^-4 rad From Rayleigh criterion, theta_res = 1.22 lambda/D = 1.22 (560 times 10^-9/2 times 106-3) = 3.416 times 10^-4 rad Here, theta_alpha theta_res so the object cannot be resolved. No (B) y = theta_res S = (3.416 times 10^-4) (0.25) = 85.4 mu m = 85 mu m (C) theta = theta_res = 3.416 times 10^-4 rad(360 degree/2 pi) = 0.0195 degree = 1.17 min = 1.2 min (D) Using the result of (C) then ""The found value is very close to the experimental value"" Option (a)"