AcademyGeometric Optics
Academy
Spherical Mirrors
Level 1 - Physics topic page in Geometric Optics.
Principle
Spherical mirrors focus paraxial rays by reflecting them from a curved surface.
Notation
\(R\)
mirror radius of curvature
\(\mathrm{m}\)
\(f\)
focal length
\(\mathrm{m}\)
\(s\)
object distance
\(\mathrm{m}\)
\(s'\)
image distance
\(\mathrm{m}\)
\(m\)
lateral magnification
1
Method
Derivation 1: Focal length
For paraxial rays, a spherical mirror has focal length half its radius of curvature.
Focal length
\[f=\frac{R}{2}\]
Mirror equation
\[\frac{1}{s}+\frac{1}{s'}=\frac{1}{f}\]
Magnification
\[m=-\frac{s'}{s}\]
Concave mirrors have positive focal length in the usual real-is-positive convention. Convex mirrors have negative focal length.
Rules
Focal length
\[f=R/2\]
Mirror equation
\[\frac{1}{s}+\frac{1}{s'}=\frac{1}{f}\]
Magnification
\[m=-\frac{s'}{s}\]
Examples
Question
A concave mirror has
\[R=0.80\,\mathrm{m}\]
Find \(f\).Answer
\[f=\frac{R}{2}=0.40\,\mathrm{m}\]
Checks
- Positive image distance for a mirror means a real image in front of the mirror.
- Negative magnification means inverted image.
- Spherical formulas assume paraxial rays.