angular separation

grouper

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

What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects?

2. Relevant equations

θ=(1.22*λ)/D

3. The attempt at a solution

I tried estimating with λ=550 nm and D=5.0 mm (pupil diameter) which appeared in another problem about viewing stars and got 1.34e-4 rad, but this was incorrect. Our book states the best eye resolution is around 5e-4 rad so I tried that as well, but it wasn't correct either. This problem must want something more concrete than an estimation but I'm not sure where to go with it.

CanIExplore

They're asking for a minimum here. According to rayleigh equation which you've written there, what criterion would minimize the angle theta?

grouper

I suppose either a smaller wavelength or a larger diameter; do you think I should be using a different λ for my estimation? If I use λ=400 nm (keeping D=5.0 mm), that yields θ=9.76e-5 rad, but that's not correct either. I got the 5.0 mm diameter from another problem, so I'm not sure adjusting the diameter will get a correct answer either.

grouper

I figured out the problem; they were asking for arcs. Wasn't indicated anywhere but I eventually gave up on this problem since it's due tonight and when it showed the correct answer it read "0.46' of arc". Would've been nice if they said that in the problem, especially considering all the other problems in our book deal in radians. Oh well.