Optical Lens Formulas
Thin-lens and magnification formulas, plus common photographic relations.
Reference
Thin lens (Gaussian)
- Thin-lens
- 1/f = 1/s_o + 1/s_i
- Magnification
- M = −s_i / s_o = h_i / h_o
- Lensmaker's
- 1/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 value
- EV = log₂(N² / t)
- Depth of field
- Narrows with larger aperture, longer f, closer subject
- Angle of view
- 2 · arctan(sensor / (2f))
- Hyperfocal
- H = f² / (N · c) where c = circle of confusion
f-stop full stops
| f-stop | Relative light |
|---|---|
| f/1.0 | 100% |
| f/1.4 | 50% |
| f/2 | 25% |
| f/2.8 | 12.5% |
| f/4 | 6.25% |
| f/5.6 | 3.13% |
| f/8 | 1.56% |
| f/11 | 0.78% |
| f/16 | 0.39% |
| f/22 | 0.195% |
Focal length feel (35 mm equivalent)
| Focal length | Class | Typical use |
|---|---|---|
| 14 mm | Ultra-wide | Landscape, architecture |
| 24 mm | Wide | Street, environmental |
| 35 mm | Normal-wide | Documentary |
| 50 mm | Normal | Everyday |
| 85 mm | Short tele | Portraits |
| 135 mm | Tele | Portrait / sports |
| 200 mm | Tele | Sports / wildlife |
| 400 mm | Super tele | Distant 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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