THE OPTICAL characteristics of a riflescope, binocular or spotting scope consist of compromises between what somebody once call the “optical triad”: magnification, eye relief and field of view.  All three affect each other, but can also be manipulated to change other optical features.

We express magnification by an “x,” with 10x meaning the view is magnified 10 times.  However, this is only an approximation, because focusing also affects the exact magnification.  You can prove this on your next trip to the range: While looking at a target through a riflescope, when you turn the rear-focus adjustment the apparent size of the target will change slightly, whether the scope is focused by turning the entire eyepiece or a ring on the rear of the eyepiece.

Field of view (FOV) is how much the area around the target we can see.  In riflescopes it’s usually expressed in feet at 100 yards, but in binoculars and spotting scopes it’s measured at 1000 yards, because they’re often used to observe at long distances.  Despite the present trend of long-range hunting, the average distance scopes are used is probably still somewhere around 100 yards.

FOV is directly affected by magnification, and again we can prove it by changing the magnification of a variable scope while looking at a target.  It’s also directly in proportion to magnification: If we look through a 3-9x scope at 3x, the view with the same scope on 6x will be half as wide.

While this is an exact rule, it doesn’t always work out that way in what might be termed “practical reality,” because magnification markings aren’t always exact.  Along with focus-ring changes, this is also why we can look through several 3-9x scopes set on 6x and see slight differences in magnification.

FOV is also affected by the ocular (rear) lens.  Essentially, the rear lens serves exactly the same purpose as a projection screen in a movie theater, except the scope is turned in the opposite direction as the theater’s projector.  Instead of looking at a film’s image in front of us, we’re looking at an image “projected” backward by the riflescope.  Just as a wider theater screen can accommodate a wider image, a wider rear lens in a scope or binocular can provide a wider FOV.

This does have limits, however.  If we place our head too close to a scope or binocular, the edge of the view in the lens disappears, leaving a smaller-diameter image inside the lens.  The same thing would happen if the screen in a theater was too close the projector, and for the same reason: The beam of light carrying the image can only be so wide, due to what’s called the exit pupil.

Most of us are familiar with the concept of the exit pupil, and how it affects the brightness of the image.  The exit pupil’s size is normally the diameter a scope or binocular’s objective (front) lens, divided by the magnification.  Thus an 8x scope or binocular with a 40mm objective results in a 5mm exit pupil.  This is important because the pupil of an average human eye contracts to about 2-3mm in bright light, and expands to 6-7mm in dim light.  As a result, a 5mm exit pupil provides plenty of light (in fact more than the eye can use) in bright light, but not quite all the light it can use in dim light, where the image appears washed-out, with little contrast.  This is exactly why some riflescopes and binoculars have objective lenses of 50mm or even more, to provide more light to the eye even in dim light.

However, there are exceptions to the objective diameter/magnification formula.  Some cheap optics have a “field stop” inside, essentially a sheet of metal or plastic with a hole smaller than the objective lens.  This cuts off the out-of-focus light rays around the edges of the FOV, making the view sharper but dimmer.  Also, most modern riflescopes have a slightly smaller exit pupil than the formula suggests, because the actual FOV is created by the erector lens system inside the scope, which is just smaller than the objective lens’s FOV.  In many older scopes the reticle shifted its visible position inside the scope, because the FOV through the erector system was larger than the FOV through the objective lens.  When the erector system was moved to adjust point of impact, the reticle visible moved inside the FOV.  And that’s the optical magic that created “permanently centered” reticles.

There are also other side-effects of exit pupil diameter that aren’t as commonly understood.  First, the exit pupil isn’t just a flat circle of light suspended in the air behind the scope.  Instead, it’s a cone of light projected out of the scope.  This is why the edge of the image blacks out when we move our eye too close to the rear lens, just as the image would only fill the middle of a theater screen if the projector’s too close.

Conversely, if we move our eye too far back from the rear lens, only a small part of the image will be visible.  Again, this is the same as a theater screen too far from the projector.  Only the middle of the image fits on the screen, and some of the actors may have their heads cut off.  (This might not be a bad idea with some actors, but that’s a different subject.)  Eye relief is the distance from the rear lens to where our eye can see the entire image, without the edges of the lens blacking out or being cut off by the eyepiece.

Scopes and binoculars of the same magnification have a different amount of eye relief, due to optical manipulation of the light-cone of the exit pupil.  A longer cone provides more eye relief, while shorter cone provides less eye relief.

In a scope on a hard-kicking rifle it would seem that a longer exit-pupil cone would be a major advantage, because it would reduce the possibility of the scope jamming into our eyebrow.  Unfortunately, a longer cone also reduces FO, because our eye is further from the “movie screen” of the rear lens.

However, there is another advantage to long eye relief in a riflescope.  The longer exit pupil also has a longer area where the exit pupil’s diameter is close to optimum for the eye’s pupil, so our eye doesn’t have to be placed exactly the right distance behind to scope to see the entire FOV.  This is often called the “eye box” and is why scopes with long eye relief are often favored for quick shooting.

However, scopes with shorter eye relief often have an apparently brighter image, especially if the ocular lens is also wide.  Both cut down on the amount of “stray” light between our eye and the image in the lens, even when ambient light is relatively dim.

This is exactly why binocular typically provide a brighter view than scopes of the same magnification and objective lens diameter, and why many night-vision riflescopes have a rubber extension on the eyepiece to block off any stray light, even from the moon and stars.  (Such extensions are even sold for typical riflescopes, and they work, especially in dim light, but apparently most hunters think they look too nerdy, even hunters who really like synthetic stocks painted in blaze-orange tiger stripes.)

This one of several reason why there were major differences in European and American riflescopes for many years.  Legal hunting hours in Europe are typically much longer than in North America, and some animals (especially native wild pigs, not the feral pigs we have over here) are often hunted all night long.  This is exactly why so many European scopes had short eye relief  — and what we would consider extra-large objective and ocular lenses.

Until relatively recently, European big game scopes were also often of higher magnification, since more magnification also provides a brighter image in dim light.  Until about 1970 the typical American scope was a fixed 4x, and even afterward higher-X scopes were often reserved for varmint hunting, or were variables turned up only on sighting-in day at the local range.  In Europe, even typical fixed-magnification big game scopes were usually at least 6x, and often 8x or 10x.  When combined with extra-large lenses, they provided more light to the eye than American scopes with smaller objectives and longer eye relief.

Of course, Europeans got away with shorter eye relief because they don’t typically shoot hard-recoiling rifles.  The biggest animals hunted in most of Europe are red stag and wild boar, neither as large as American elk, and even the “moose” of Scandinavia are relatively small.  And except for some varmints (including feral pigs), North American don’t usually hunt at night — and when we do, we can often use illuminated-reticle and night-vision scopes, illegal in much of Europe.

Neither system is better or worse.  Instead, they’re just different manipulations of the optical triad, due to different hunting conditions.  But about 15 years ago the head of the American advertising agency for a well-known European optics company bragged that the Euro-company’s scopes had 30% more FOV than the most popular American brand of riflescope.  To anybody who knows optics, this was a sort of “duh” statement, like saying a compact car gets better mileage than the average half-ton pickup.  The guy was also a nitwit in almost every way possible, so I delighted in pointing out that the American scope had 30% longer eye relief.

One other rarely-mentioned aspect of the triad is parallax, the apparent shift of the reticle across a target at certain ranges.  As American scopes became larger over the past quarter-century or so, we became used to a parallax-adjustment knob on the side of scopes above 10x or so.  But parallax is also affected by objective lens diameter, because it affects exit pupil size.

Parallax can’t exist as long as our eye is centered perfectly behind the scope.  One way we can accomplish this backing our eye up until the outer edge of the FOV is blacked out, then consciously centering the reticle in the visible FOV.  However, a small exit pupil also reduces parallax, since it doesn’t allow our eye to wander very far off the optical center of the scope.

When a typical 3.5-10×40 variable is set on 10x the exit pupil is only 4mm in diameter, our eye can only be 2mm off-center in the scope.  If we increase the diameter of the objective lens to 50mm or 56mm, to increase the diameter of the exit pupil and provide a brighter image, our eye can also be further off-center and still see the entire FOV, increasing potential parallax.

In recent years at least some variables with a top end of 10x have featured objective lenses under 40mm, partly because it reduces parallax.  With a modern optical system using interior baffling and high-quality, multi-coated lenses the image is still usably bright, despite the relatively small exit pupil.

Since binoculars and spotting scopes don’t recoil, we can get away with much shorter eye relief and hence a larger field of view, especially helpful with the high magnification of many modern spotting scopes.  However, many humans require slightly longer eye relief, because they wear glasses, preventing the binocular or scope from being backed up right next to the eye.  This is why most of today’s binoculars and spotting scopes offer easily adjustable eyecups, though some have longer eye relief than others.

The optical triad always results in optical compromises, but if we understand those compromises we can pick the scope or binocular with the best combination of optical features for our particular use.