resolution of distant light sources

grouper

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

How far away can a human eye distinguish two car headlights 2.1 m apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 mm and a wavelength of 550 nm. 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 where D=diameter

3. The attempt at a solution

If θ=2sin-1(0.5d/l) where d=distance between objects and l=length/distance to objects, then θ=(1.22*λ)/D with λ550e-9 m and D=0.005 m and l=2.1 m yields l=8.9658e5 m. This is incorrect though and I'm not sure where I went wrong. Any help is appreciated, thanks.

cepheid

That's almost 900 km. The first thing you should do when solving physics problems is to ask yourself whether the answer you obtained makes any sense. Is it reasonable?

You must have made some sort of algebraic error somewhere. We can't really help you track it down unless if you show us the steps in your solution.

grouper

Yes, I recognized that my answer was way off. Which is why I was confused, because I couldn't find the mistake earlier in my work.

And yes, I must have made some sort of calculator error because I just tried it again and got 15648 m, which is much more reasonable (and also the correct answer). Thanks for the help.