Solving Grating Resolution Homework for Skyscraper Distance

[Gee Wiz]

Homework Statement

Considering larger objects, a skyscraper has two tall antennae separated by 3 meters. Each antenna has one blue and one red light. You can resolve the two blue lights but not the red ones.

Assume that your pupils have a diameter = 2 mm at night, and that blue light's wavelength is 475 nm, while red light's wavelength is 650 nm.
Approximately how far are you from the skyscraper? (Also assume that you have 'perfect vision' limited only by diffraction.)

Homework Equations

θ=1.22λ/D

Δλ/λ=1/(mN)

The Attempt at a Solution

I know the answer is 10km, but I don't know how to get that. I was trying to find a way to determine the resolution requirement, or something like that.

 

[Simon Bridge]

There is a minimum angular separation that you can resolve two objects - it depends on the wavelength of the light and the diameter of the aperture. You should have some notes on this under "resolving power".