The Optical Triangle — “Nothing for Free” (scopes)

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The Optical Triangle — “Nothing for Free”

by Gary Chang

Originally published 12/2009

Have you ever wondered why different scopes have different eye relief, or why your eye needs to be closer to the ocular lens when you boost the power? These questions and other specific properties of rifle scopes relate to what is technically called the optical triangle. Basically, these properties dictate that, when the power is increased (causing the field of view to be reduced), eye relief becomes more critical and requires more exact and closer eye placement. Allow me first to define these terms:

  • Eye relief: Distance between the viewer’s eye and the ocular (rear-most) lens of the scope. Critical eye relief means that your eye has to be in nearly the same spot for the full image to avoid having the edges of the scope black out. “Liberal” eye relief means that your eye has wider latitude before blackout.
  • Power/magnification: To increase or reduce the magnification of the viewed image. Although there are fixed power scopes, most marketed now are variable; the most popular magnification is 3-9X.
  • Field of View (FOV): Expressed in feet at 100 yards, this indicates how wide a diameter can be seen at any given distance. For example, if a 4X typically has a 30-foot FOV at 100 yards, it only allows for 15 feet at 50 yards (or half the distance).

These 3 properties form the optical triangle and are governed by the laws of physics. In glass, you don’t get anything for “free.” If you’ve ever wondered why your Leupold glass might have more critical eye relief than a similarly powered Burris, it is because that is how the engineers juggled the properties to suit their idea of optimum.

Related to eye relief is the exit pupil. This is usually expressed in millimeters and can be mathematically calculated by dividing the objective lens (forward lens) by the power. Because the exit pupil changes as power is shifted, head placement becomes more critical with an increase in magnification and results in a decrease of light available to your eye. The human eye cannot use more than 7 mm of this “ball of light.” Young eyes cannot dilate more than 7 mm. At ages over 50, this shrinks to 5 mm as our eyes lose flexibility.

There is one benefit of having a larger exit pupil than the eye can use: because the ball of light is conical, if your eye is anywhere on the fringe of the ball, the image will be visible. This can be evidenced by comparing a mini/compact scope to one of the same power but full-sized. Although sleeker and lighter in weight, these downsized rifle scopes require much more critical head placement.

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