# Smallest Angular Separation

1. Nov 12, 2015

### Barry Melby

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
theta_r = sin(theta_r) = 1.22(wavelength/d)

3. The attempt at a solution
theta_r = 1.22(400*(.000000001)) / (6*.001) = .0000813

This is incorrect. Where have I gone wrong?

2. Nov 12, 2015

### 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...

 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: Nov 12, 2015