So is there then a real-world metric for angular resolution for comparative apertures and powers that can be worked out like a Rayleigh and Dawes? There should be anyway.
Your thoughts?
The Rayleigh and Dawes limits carry the same meaning for binoculars as they do for telescopes, since they're very simply derived from the aperture alone. Those figures don't account for magnification in any way. You can't observe Rayleigh and Dawes doubles with fixed mag binos because of their relatively low magnification.
I'm not entirely sure what the question here is, but I assume it's something along the lines of how close of a double can you observe with a given binocular of a certain aperture and magnification?
A brief aside before trying to answer your question:
The Dawes limit for an 50mm binocular is about 2.32 arc seconds. Even if you were using a 20x50 binocular, the apparent separation (discussed in the next paragraph) of a 2.32" double is 46.4". The theoretical resolving ability of the human eye is about 60" (this number is too low for our case, and exceptionally few if any people can split a double star with a 60" separation to their naked-eye). The point is, fixed mag binoculars, in the formats actually available to consumers, won't make Dawes or Rayleigh splits even in theory.
To the question as I understand it: because binoculars lack the magnification to be diffraction limited, you can essentially toss aperture and the associated Rayleigh and Dawes limits out the window (sort of, obviously aperture has some relevance to observing double stars with binos in general). The remaining factors (ignoring magnitudes and delta magnitude of the double star in question, which are also obviously relevant, but I'll ignore for this discussion) are magnification and visual acuity of the observer. So, the real determining factor is the apparent separation of the double. Take a 70" double, and use a 10x bino. The apparent separation is 700" (70" x 10). This would be a very easy split for most people. How low of an apparent separation you can get to will depend on the specific double (we're ignoring that for now), potentially the quality of the bino (also going to ignore that for now), and the observers visual acuity. Making an assessment of how tight a double you can split with a given binocular should be done with them mounted. Assuming the double contains two stars of the same or similar magnitude (and they aren't excessively bright or faint), and that the binoculars used are of good quality, I would suggest most people are going to be capable of splitting a double with an apparent separation of around 180-200 arc seconds. Some people will be able to go closer, some won't be able to go that tight. What you can do is something you'll only discover with experience.
*To determine apparent separation, multiply the actual separation by the magnification of the bino.
*To determine the actual separation that yields a desired apparent separation with a given bino - divide the desired apparent separation by the magnification of the bino.
Edited by JoeFaz, 07 July 2025 - 07:37 AM.
