When calculating angular resolution, is it correct that having a SMALLER number results in GREATER angular resolution? For example, is 26.25" better resolution than 2625"? Using the formula .25"(lambda in micrometre/diamter in meters), it would make sense to me that the larger the diameter, the smaller the answer, thus the greater the resolution. I just want to be sure I understand this correctly. Also, out of curiosity, why are we multiplying by .25"? This is the formula my book gives me...but is this always a constant for this formula? Thanks!
Yes, the number gets smaller with better resolution. Think of it this way - the angular resolution tells you the minimum angular separation at which two point sources could be resolved, or in other words, seen without blurring together. In your example, an angular resolution of 26.25" means that two point sources 26 arcseconds apart could barely be resolved. The constant is just a conversion factor to make the numbers come out right for the units you're using (arcseconds, microns, meters). The general formula is sinθ = 1.22λ/D - the 1.22 comes from the circular geometry of a point source being imaged by a telescope.
You may have been 'thrown' by the use of the English language, I think. The word "higher" means 'better' in this context and does not mean a bigger number of minutes of arc. It is used more in the sense of 'pixels per inch' - as with TV monitors and printers, where 'more' means better resolution.