A Breakdown of the Relationship Between Rifle Scope Magnification vs. Distance

A Breakdown of the Relationship Between Rifle Scope Magnification vs. Distance

The relationship between rifle scope magnification vs. distance is relatively straightforward once rifle scope magnification is explained. The first step to explaining rifle scope magnification is understanding how to read rifle scope magnification from a scope’s specification.

A rifle scope specification includes two numbers. The first number identifies the magnification while the second number identifies the diameter of the objective lens. Thus, a specification of 8.5×50 describes a scope with 8.5× magnification and an objective lens that is 50 mm in diameter. Variable magnification scopes have a specification that describes the range of magnifications provided by the scope. For example, a scope from our Elite Tactical™ line has the magnification 3.5-21× which means that the scope can magnify anywhere between 3.5× and 21×.

Rifle Scope Magnification Explained

The magnification is a physical property of the scope. That is, it is defined by the thickness, curvature, diameter, and material of the lenses and their coatings. Once the physical properties of the lenses and their coatings are known, a set of equations defines the optical properties of those lenses.

The lenses inside a scope perform three primary purposes.

  • Magnify the target: The objective lens captures light reflected from the target and bends the light to create a magnified image of the target. Some scopes use multiple lenses to magnify the target.
  • Invert the magnified image: The image generated by the objective lens is inverted. An erector assembly contains two lenses that flip the image so that it is right-side-up. The erector assembly can also contain the additional magnifying lenses for a variable magnification scope.
  • Focus the image: The ocular lens focuses the image that has been magnified and flipped right-side up for your eye. The diameter of the ocular lens also determines the eye relief – the distance between the scope and your eye from which you can see the full, focused image.

The Magnification Equation Determines the Size and Distance of the Magnified Image

The image viewed through the ocular lens is just that – an image. It is, in this respect, a reflection of reality rather than reality itself. The relationship between the image and the target is linear and proportional. Specifically, the magnification defines the ratio between the focal length of the ocular lens and the focal length of the objective lens. In application, this means that the magnification tells you how the image will differ from the target. A target viewed through a 3× magnification scope will appear to be three times closer than its actual distance – targets at 300 yards will appear as if they were 100 yards away.

As the magnification increases, the apparent distance to the image decreases in direct proportion. Thus, doubling the magnification from 3× to 6× will cause the target’s image to appear half as far away.

As a corollary to this equation, the height of the target will also increase in proportion to an increase in magnification. This means that a doubling of magnification from 3× to 6× will not only halve the apparent distance to the target but also double its apparent size.

Physical Limitations of Magnifying Lenses

Magnification does come with trade-offs. There are many optical limitations and types of distortion that are tied to magnification.

1. Chromatic Aberration

Chromatic aberration or fringing can occur with any lens, but worsens as magnification increases. You see the cause of chromatic aberration when you see a rainbow or view light through a prism – different wavelengths of light interact with a raindrop or prism differently. This causes white light to break up into its constituent colors. The result is that an image viewed through a lens without correction for chromatic aberration can appear blurry or fringed with purple.

2. Field Curvature

In scopes with low magnification, field curvature can cause blurriness at the edges of the image. At low magnification, the sharpest focus for the image is closer to a sphere than a plane. Consequently, a target and reticle that are sharp near the center of the image are blurry at the edges of the image.

3. Spherical Aberration

As magnification increases, spherical aberration may arise. Spherical aberration happens because light is bent more at the edges of a lens than at the center of the lens. This means that the light from the edges of the lens meets at a slightly different focal point than the light passing through its center. Spherical aberration has the same effect on the image as field curvature – the image may appear blurry at the edges when the center of the image is in focus.

4. Field of View

Field of view can be calculated by dividing the diameter of the objective lens by the magnification. As the magnification increases, the field of view will decrease proportionally since the diameter of the objective lens is a fixed number. This means that less area will be visible as magnification increases.

5. Dimness

As lenses thicken, or more lenses are included in the scope, more light will be reflected and absorbed rather than transmitted. Even coated lenses will transmit less than 100% of the light incident on the lens. As a result, higher magnification scopes will produce dimmer images than lower magnification scopes.

Making a Choice – Rifle Scope Magnification vs. Distance

There is a saying that you should choose the magnification that is just enough for you to hit the target. In other words, too much magnification brings in drawbacks, such as weight, complexity, and distortion, that produces diminishing returns for the rifle scope. In fact, many shooters find that they need no more than 10× magnification for targets up to 500 yards away. Many hunters settle on magnification between 4× and 6× since most shots taken during deer hunting season will fall between 100 and 200 yards.

On the other hand, shots taken at longer ranges, shots at smaller targets, or shots from more powerful rifles may call for higher magnification. Smaller targets, particularly stationary targets in precision rifle shooting competitions, will be less subject to losses in field of view and less subject to distortion.

Bushnell’s® Elite Tactical rifle scopes range in magnification from 1× to 30×. Review these and other Bushnell® rifle scopes to find a magnification appropriate for the distance to your anticipated targets.