Calculate lens power, focal length, diopters, and other optical properties
Optical power measures the ability of a lens or mirror to converge or diverge light.
| Optical Element | Focal Length | Optical Power | Application |
|---|---|---|---|
| Human eye lens | 1.7 cm | 58.8 D | Vision focusing |
| Camera lens | 50 mm | 20 D | Photography |
| Reading glasses (+1.0) | 100 cm | 1.0 D | Presbyopia correction |
| Myopia glasses (-4.0) | -25 cm | -4.0 D | Nearsightedness correction |
| Telescope objective | 100 cm | 1.0 D | Astronomy |
| Magnifying glass | 10 cm | 10 D | Magnification |
Optical power measures a lens's ability to converge or diverge light. It is expressed in diopters (D), which is the reciprocal of focal length in meters.
Diopter Definition: D = 1 / f
Where f is focal length in meters
Convex Lenses: Converging lenses with positive power
Used to correct hyperopia (farsightedness)
Concave Lenses: Diverging lenses with negative power
Used to correct myopia (nearsightedness)
Magnification: Ratio of image size to object size
m = -v / u = f / (f - u)
Negative power lenses (-0.25D to -20D)
Positive power lenses (+0.25D to +20D)
Cylindrical lenses (0.25D to 6.00D)
Lens power (P) and focal length (f) are inversely related:
P = 1 / f
Where:
Examples:
| Focal Length | Optical Power | Lens Type |
|---|---|---|
| 0.25 m | +4.00 D | Strong convex |
| 0.50 m | +2.00 D | Convex |
| 1.00 m | +1.00 D | Weak convex |
| -0.50 m | -2.00 D | Concave |
| -1.00 m | -1.00 D | Weak concave |
For two lenses in contact:
Ptotal = P₁ + P₂
For two lenses separated by distance d:
Ptotal = P₁ + P₂ - (d × P₁ × P₂)
Where:
Example:
Lens 1: +4.00 D
Lens 2: -2.00 D
Distance: 0.1 m
Ptotal = 4 + (-2) - (0.1 × 4 × -2) = 2 - (-0.8) = 2.80 D
Magnification (m) relates to optical power through the lens formula:
m = -v / u = f / (f - u)
Where:
For a given object distance, higher power lenses produce greater magnification.
Example for u = -0.25 m:
| Power | Focal Length | Magnification |
|---|---|---|
| +2.00 D | 0.50 m | 2.00 |
| +4.00 D | 0.25 m | 1.00 |
| +8.00 D | 0.125 m | 0.50 |
Refractive index (n) directly affects lens power through the lensmaker's equation:
P = (n - 1) × (1/R₁ - 1/R₂)
Where:
Higher refractive index materials allow thinner lenses with the same power.
Common materials:
| Material | Refractive Index | Advantages |
|---|---|---|
| Crown Glass | 1.52 | Low cost, scratch resistant |
| CR-39 Plastic | 1.50 | Lightweight, impact resistant |
| Polycarbonate | 1.59 | Impact resistant, UV protection |
| Trivex | 1.53 | Excellent optics, impact resistant |
| High-index Plastic | 1.60-1.74 | Thinner lenses for high prescriptions |