What Is the Smallest Angular Separation the Human Eye Can Resolve?

  • Thread starter Thread starter Barry Melby
  • Start date Start date
  • Tags Tags
    Angular Separation
Click For Summary
SUMMARY

The smallest angular separation that the human eye can resolve is determined using the formula theta_r = 1.22(wavelength/d), where the pupil radius is 3.0 mm and the wavelength of violet light is 400 nm. The calculated value of theta_r is approximately 8.13 x 10-5 radians, which translates to about 17 arcseconds. This value aligns closely with the theoretical limit of 2 x 10-4 radians for acute vision under optimal conditions, as noted by Hyperphysics. Factors such as color sensitivity may affect the perception of closely spaced objects.

PREREQUISITES
  • Understanding of angular resolution and diffraction limits
  • Familiarity with the formula for resolving power in optics
  • Basic knowledge of light wavelengths, particularly in the visible spectrum
  • Concept of pupil diameter and its effect on vision
NEXT STEPS
  • Research the effects of diffraction on optical systems
  • Explore the relationship between pupil size and visual acuity
  • Study the impact of different wavelengths of light on human vision
  • Investigate the physiological limits of human eyesight under various conditions
USEFUL FOR

Optics students, vision scientists, and anyone interested in the physiological limits of human vision and angular resolution in optical systems.

Barry Melby
Messages
31
Reaction score
0

Homework Statement


For an eye in which the pupil has a radius of 3.0 mm, what is the smallest angular separation that can be resolved when two violet (λ = 400 nm) objects are placed side by side?

Homework Equations


theta_r = sin(theta_r) = 1.22(wavelength/d)

The Attempt at a Solution


theta_r = 1.22(400*(.000000001)) / (6*.001) = .0000813

This is incorrect. Where have I gone wrong?
 
Physics news on Phys.org
Who says it's not correct ? I get what you get using that formula.

When I Google angular resolution and look at the picture , then violet at 6 mm aperture shows something that looks around 15 arcsec, and sure enough 8.13 x 10-5 * 180/##\pi## = 17/3600 .

My eyes sure don't dissolve two spots on a 10 m far wall that are 0.8 mm apart, but perhaps that isn't the idea anyway...

[edit] another contribution: Hyperphysics mentions 2 x 10-4 radians for "Most acute vision, optimum circumstances" -- within a factor 2 of the physical limits imposed by diffraction.

The only thing I can think of that would spoil the fun is that blue and violet are difficult colours for human eyes, but I don't have anything quantitative on that.
 
Last edited:

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
5K
Replies
3
Views
5K
  • · Replies 6 ·
Replies
6
Views
8K
  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 2 ·
Replies
2
Views
8K
  • · Replies 7 ·
Replies
7
Views
4K
Replies
3
Views
3K
  • · Replies 1 ·
Replies
1
Views
6K
  • · Replies 2 ·
Replies
2
Views
25K