On a compound bow the scope lens should be chosen for the archer's draw length and eyesight: the same lens does not magnify the same way for everyone

The summary today

The only work on the subject is a 2010 optics paper by two authors from the optometry department of the University of Johannesburg, and it contains no measurements: it applies the lens equations to the two ways a compound archer can magnify the target. With a lens on the sight alone, magnification depends on the archer's refractive error: by the calculation, a hyperope of one dioptre sees the target upright and magnified about twice with a +0.50 lens, while for someone with normal vision the theoretical magnification is nil and the actual effect depends on accommodation, which fades after about the age of 40. With two lenses, one on the sight and one in the peep, draw length is what matters: with the same +2 dioptre front lens an archer with a 29 inch draw gets about 1.7 times magnification with the image upside down, one with a 24 inch draw gets 5 times with the image upright. The reasoning is consistent, but it is calculation and nothing more: no archer has looked through those lenses, and in the hyperope example the printed values work out for a distance of one metre, not the 80 centimetres stated.

Also phrased as: "compound scope lens"; "scope magnification"; "peep sight lens"; "clarifier"; "lens power and draw length"; "lens and presbyopia in archery"

Evidence

• 2010
  For Model Published later

  Two-lens system, on the sight and in the peep, calculation only: with the same +2 dioptre front lens, a 29 inch draw (about 0.80 m between the lenses) gives a 3.33 dioptre ocular lens and a magnification of minus 1.67, meaning an upside-down image; a 24 inch draw (about 0.40 m) gives minus 10 dioptres and a magnification of 5, with the image upright.

  Optical lenses and magnification in archery · B. Strydom, J. T. Ferreira

• 2010
  For Model Published later

  Single-lens system: for a 1 dioptre hyperope with the lens at 0.80 m the authors give a +0.50 lens and a magnification of 2, with an upright image and sharpness tied to accommodation; for someone with normal vision the theoretical magnification is nil, and the actual effect depends on accommodation, which fades with presbyopia, evident from about the age of 40. Recalculated with the paper's own equations, at 0.80 m the hyperope's values are about +0.56 and 1.8: the printed ones correspond to a distance of one metre.

  Optical lenses and magnification in archery · B. Strydom, J. T. Ferreira

• 2010
  Context Model Published later

  Drawing on the physiological optics they cite, the authors give a peep or pupil size between 2 and 5 millimetres as the window for best acuity: below 2 diffraction takes over, above 5 spherical aberration, and a smaller aperture extends depth of field. No measured data.

  Optical lenses and magnification in archery · B. Strydom, J. T. Ferreira

Status history

1. 2010 Transferred Two authors from an optometry department apply the lens equations to the compound bow, with no measurements. With a single lens, magnification depends on eyesight: a hyperope of one dioptre sees about twice as large with a +0.50 lens, someone with normal vision in theory not at all. With two lenses, on the sight and in the peep, it depends on draw length: with the same +2 dioptre lens, 1.7 times with the image upside down at 29 inches and 5 times upright at 24. The claim rests on an optical model, with no archers involved: transferred.

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