The Optics Formula: An Introduction

What by What?
The “Optics Formula”: An Introduction
Why Those Two Numbers With An “X” In The Middle Are Such A Big Deal
(Magnification by Diameter of the Objective Lens (the end away from your eyes)

Every binocular has this handy “mathematical formula” attached to it (and usually printed right on the binocular). It tells you an essential “story” about that binocular—but not the whole story. The good news is that knowing what the numbers represent allows you to eliminate a huge number of available optics from your purchase decision, making the buying process easier and less confusing.

The first, or left number is the magnification, or power, of the binocular (8X = 8 power). Simply stated an 8 power binocular makes the object you’re looking at appear 8 times closer than it does with the naked eye. Since presumably you’re using the binocular to get a closer look, this number is key, but as is true so often in life, bigger doesn’t necessarily mean better. 

True, with a higher power binocular you are magnifying to a greater degree your target image, but you’re also magnifying any movement of the holding platform of the device—meaning you. So with an 8-power binocular you are also magnifying the image-distorting effect of such things as hand tremor (which everyone has whether they know it or not) and the beating of your heart (which I assume you have as well). So the target image is larger, but the quality of that image in terms of detail you can discern changes little, if at all.

Higher magnification also narrows the field of view (discussed elsewhere on this site) and decreases brightness, thus further limiting its advantages. It’s for these reasons that I strongly advise limiting the magnification to 8-power with your first or primary binocular (see “Optics Formula, Rule 1).

The second, or right, number is the diameter in millimeters (metric system alert!) of the objective lens, which is at the opposite end of the barrels from the ends to which you’re putting up your eyes. Since this is where the light enters the binoculars before traveling through the barrels and exiting the other side (the ocular lens), this is a jumping-off point to how bright the image will be—but it is by no means the only determining factor (I explore brightness factors in another post). As with magnification, bigger isn’t always better, but it’s often heavier, owing to the dense, heavy optical glass down at that end. And that, more often than not, is a really big deal—see “The Most Important Binocular Spec” elsewhere on this site.

For arithmetic aficionados there’s a measure of brightness called “exit pupil,” expressed in millimeters, that can be calculated by dividing the magnification into the objective lens diameter: for a 7 X 42 the exit pupil would be 6 mm; an 8 X 32 optic would have an exit pupil of 4mm (and if you’re like me, to figure out the EP of a 8.5 X 42 you’ll need a calculator). Or just skip the math, hold the binocular up to a light source and look at the ocular (eyepiece) lenses; that light round dot in the middle of each ocular lens is the exit pupil, and now you can figure out its diameter! Better yet, stack an 8 X 32 on top of a 7 X 42 and look at the eyepieces—the round dots on the 7X (6mm) are noticeably larger than those on the 8X (4mm). That’s the column of light hitting your eyes—a vivid demonstration of how much brighter the 7 X 42 is! Congratulate yourself, you’ve just done both Science and Math!

You’ll see binocular magnifications (first number) as low as 6x (3 or 4x if you’re looking at opera glasses) and as high as 15x (more if they’re tripod-mounted). You’ll see objective lens diameters as low as 20 (compact or pocket binoculars) and as high as 56 (otherwise known as too-heavy-for-humans-to-use binoculars). That gives you a lot of potential (magnification) X (objective lens diameter) combinations to sift through when you’re deciding on a binocular, but good news! I help you eliminate a ton of them in the following posts on the Three Optics Formula Rules.