Mirror Focal Length⚠ unverified
Physics / Optics · Compute the focal length of a spherical mirror
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| R | R | m | 1.0 | Radius of curvature of the mirror |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | f | m | Focal length, in metres (m) |
The science & history
Understanding the Parameters
- $R$ — larger radius → longer focal length (weaker mirror).
- $f$ — focus of paraxial rays parallel to the axis.
Derivation (Approaching a Proof)
Geometry of reflection: a ray parallel to the axis reflects through the focus; relating triangle similarity on a spherical surface of radius $R$ gives $f = R/2$ in the paraxial limit ($\sin\theta\approx\theta$).
History
Spherical mirrors predate lenses in light concentration; $f=R/2$ is standard geometric optics.
Related Concepts: Lensmaker's Equation, Lens Power, Lens Magnification
Notes: Registry calculator mirror-focal-length (unverified). Paraxial spherical mirror.