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

[Barry Melby]

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?

 

[BvU]

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.