For a compound shooter, sights and scopes are important, and a subject of endless discussion, I hope to perhaps add a little clarity (hah) by recounting my own experiences, mistakes and conclusions. But for now, here is an article on scope lenses, maybe too much for some, but for those like me who have to know how something works, I hope it helps.
Scope magnification– it’s complicated!
Confused about scope magnification? you are not alone, why is it sometimes expressed in diopters and sometime as X power?. Unfortunately there isn’t really any way to translate one into the other with any accuracy because the magnification and the diopter of a lens are two different things.
The diopter of an archery target scope is simply the focal length of the scope divided into one meter. To find the focal length of a scope, focus the sun’s rays through the lens onto a piece of paper then measure the distance between the paper and the lens; that’s the focal length. To find the diopter, divide that figure into one. Thus if your scope focuses sunlight to a fine point when it is 2m away from the paper you divide 2 into 1 to get a diopter of .5.
Most scope manufacturers use a semi-standardised and very misleading scale of diopter (d) to magnification (X) of .25d=2X, .50d=4X, .75d=6X and 1d=8X. Unfortunately, these ratios have only a vague relationship to actual magnification, which is a bit more complicated because it depends on the distance of the scope from your eye. The actual magnification is determined by multiplying the distance of the lens from the eye by the diopter, subtracting the result from one, then dividing that result back into one. Thus if your .5 diopter 4X lens is 800mm away from your eye when you are at full draw, the distance times the diopter would be .8 X .5 =.4. When .4 is subtracted from one you get .6 , and when .6 is divided into 1 you end up with an actual magnification of only about 1.66X, which (it goes without saying) is a lot less that 4X. If an archer with short arms used that same .5 diopter lens on a target sight without an extension so that the lens was only 700mm from the eye, the result would be a magnification closer to 1.5X. Now if an archer with long arms were to shoot with the same scope 900mm from his eye, the magnification would be around 1.8X.
You’re right! Scope magnification is complicated. Just remember that the magnification rating of an archery target scope is not the same as the magnification rating of a pair of binoculars and that the archer with a short draw length using no sight extension is going to need more magnification to get the same results as a shooter with a long draw length and a long sight extension.
Now read my article on peeps as the two subjects are related.