A significant characteristic of an optical viewing instrument is the diameter of the exit pupil. The exit pupil is the circular patch of image-forming light the instrument presents to your eye. If you point a riflescope toward a brightly lighted wall or a patch of clear sky (but not at the sun!) and position your eye about 10 inches from the eyepiece, along the optical axis, you will see a bright disc of light in the center of the field. That disc is the exit pupil. The larger it is, the brighter the viewing will seem, because more of your eye will be bathed in light.
All other conditions remaining constant, changing the magnification to 6X reduces the exit pupil to 3.3mm.
You can calculate the size of a scope's exit pupil by dividing the effective objective diameter in millimeters by the magnification. For a 4X 32mm hunting scope, divide the 32mm objective size by 4 and you find that the exit pupil is a generous 8mm in diameter. With a 6.5-20X 50mm target/varmint variable scope, the exit pupil ranges from a large 7.7mm at 6.5X to a smallish 2.5mm at 20X. In a low-light situation, all other factors being equal, a lower magnification setting will provide seemingly brighter viewing than a higher one.
It is tempting to conclude that the largest obtainable exit pupil is the most desirable. But that's not always the case. The catch is that the pupil of a normal human eye opens to a maximum diameter of 5mm to 7mm, depending on the individual, even in extremely dark surroundings. Exit-pupil diameters that exceed about 7mm deliver more light than your eye can accept.
On the other hand, large exit pupils offer advantages beyond simply flooding your eye with light. With riflescopes, one of the blessings of a large exit pupil is greater freedom to position the eye with respect to the optical axis. When you must mount the rifle quickly for a now-or-never shot, you don't have the luxury of placing your eye behind the ocular with the exquisite precision a target shooter can lavish on finding the sweet spot of a 2mm or smaller exit pupil. You'll be truly grateful for the chance a large exit pupil gives you to see what you need to see, even if your eye is less than ideally located.
Looking through a 1.5-6X 20mm variable-power riflescope set to 1.5X reveals a sizeable 13.3mm exit pupil (crosshair is too out of focus to show in photo).
Another benefit of a suitably large exit pupil is the ability to see the scene clearly, without eyestrain. If you compare two scopes of equal optical quality, the one with the larger exit pupil will probably strike you as more preferable. Both will give you the same visual information, but one will make your eye work less.
Having praised generous exit pupils, I must confess that the riflescopes I use most often are fixed-power target models with exit pupils from about 1.1mm to 1.6mm. In daylight ranging from heavy overcast to bright sun they do what I need done.
One cautionary note regarding the exit pupil. There is no correlation between the size of a scope's exit pupil and overall optical quality. Some superb scopes have small exit pupils and some real dogs have very large ones. Exit-pupil calculation is a useful tool in selecting scopes, but it isn't the whole toolbox. You should consider everything and then ultimately believe your own eyes.