Science & Engineering

Optical Lens Formulas

Thin-lens and magnification formulas, plus common photographic relations.

Thin lens (Gaussian)

Thin-lens1/f = 1/s_o + 1/s_i
MagnificationM = −s_i / s_o = h_i / h_o
Lensmaker's1/f = (n − 1)(1/R₁ − 1/R₂)
Power (diopters)P = 1/f (meters)

Camera / photography

f-number N= f / D (focal length / aperture diameter)
Exposure valueEV = log₂(N² / t)
Depth of fieldNarrows with larger aperture, longer f, closer subject
Angle of view2 · arctan(sensor / (2f))
HyperfocalH = f² / (N · c) where c = circle of confusion

f-stop full stops

f-stopRelative light
f/1.0100%
f/1.450%
f/225%
f/2.812.5%
f/46.25%
f/5.63.13%
f/81.56%
f/110.78%
f/160.39%
f/220.195%

Focal length feel (35 mm equivalent)

Focal lengthClassTypical use
14 mmUltra-wideLandscape, architecture
24 mmWideStreet, environmental
35 mmNormal-wideDocumentary
50 mmNormalEveryday
85 mmShort telePortraits
135 mmTelePortrait / sports
200 mmTeleSports / wildlife
400 mmSuper teleDistant wildlife

Notes

  • Crop factor (sensor smaller than full-frame): multiply full-frame focal length to get equivalent field of view (APS-C ~1.5×, Micro 4/3 ~2×).
  • Diffraction limits sharpness at very small apertures — f/16+ on full-frame softens noticeably.
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