Question

Problem 26.49: Resolution of the eye, I.

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 object a person can see clearly at his near point of 22.5 cm with a pupil 2.25 mm in diameter and light of wavelength 498 nm ? (To get a reasonable estimate without having to go through complicated calculations, we'll ignore the effect of the fluid in the eye.)

Part B

Based upon your answer, does it seem that diffraction plays a significant role in limiting our visual acuity?

Answer 1

Part A

Using Rayleigh's criterion, what is the smallest object a person can see clearly at his near point of 22.5 cm with a pupil 2.25 mm in diameter and light of wavelength 498 nm ? (To get a reasonable estimate without having to go through complicated calculations, we'll ignore the effect of the fluid in the eye.)

Limiting angle of resolution for a circular aperture

Where:
wavelength.
  Pupil Diameter

evaluated numerically

now with the minimum angle

where:

   size of the smallest object that can see

distance

for very small values can say that.

Finally

the smallest object a person can see clearly

Part B

Based upon your answer, does it seem that diffraction plays a significant role in limiting our visual acuity?

The principles that govern the diffraction allow to understand the factors that affect our vision and to estimate, our visual ability and use it to study in order to design equipment that will allow us to improve it.

It also allows us to understand our vision mainly limits the diameter of our pupils.