Focal length and radius
Intermediate
Focus is half the radius of curvature.
f = R/2For a spherical mirror f = R/2 for paraxial rays. Large aperture rays focus elsewhere (spherical aberration); parabolic mirrors avoid this.
R = 40 cm: f = 20 cm.
Sign: concave f is negative in Cartesian convention.
In more detail
The focal length of a spherical mirror is half its radius of curvature, f = R/2. It is the distance from the mirror at which parallel rays converge or appear to diverge from.
Real-world uses
- Mirror manufacturers specify focal length to match design needs.
- Telescopes use long focal lengths for magnification.
- Telescope makers choose a mirror's radius of curvature to set its focal length, which is half the radius.
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Frequently asked questions
Is the focal length the same as the radius?
No, the focal length is half the radius for mirrors.
Does the focal length change with mirror size?
Not for a spherical mirror of a given radius, though large mirrors can show aberrations.
Why is the focus half the radius?
For mirrors with a small angle, parallel rays meet at the point halfway between the centre and the surface.
Related topics in Optics
Spherical mirrors · Mirror equation · Magnification of a mirror · Refraction of light · Refractive index · Snell's law