Okay, I’m pretty sure that’s called the half-angle, not the half-angle aperture. I solved for the combined numerical apertura of the condenser and the objective, which is obviously not right.Not quite. How I understand it, the half numerical aperture is an angle measurement, so the max value would be 90 (180 would be the max for the angular aperture, and would occur when the cover slip is touching the objective lens). So, it'll be larger than 2.745. To solve this problem, you would first solve for the numerical aperture with the resolution equation (resolution = wavelength / 2*NA) then use that to solve for one-half angular aperture in the numerical aperture equation. So the NA is 1.125, and the one-half angular aperture is 47.95 degrees. You can also use the resolution equation resolution = 1.22*wavelength / numerical aperture, which I think is what you were using (except in this problem I was talking about the NA of the entire microscope, didn't factor in that both the condenser and the objective would have a numerical aperture; probably should've specified that). I think the formula varies based on the microscope, but I'm not sure.
I had never heard of that equation you listed. I’ll put it in my notes — thanks. Is the NA in that equation of the whole microscope or just the objective?