Mirror Equation Calculator
Focal length is half the radius. Sign does the rest.
Work out Mirror Equation. Focal length is half the radius. Sign does the rest. Names the misconception directly.
Image distance
0.15 m
Real, inverted and reduced
A spherical mirror's focal length is half its radius of curvature — positive for concave, negative for convex. Beyond that sign, the equation is identical to the thin lens one, which is a genuine unity rather than a coincidence: both describe how a surface bends rays toward or away from an axis. A convex mirror always produces a virtual, upright, reduced image, no matter where the object sits. That is why they are used as wing mirrors and in shop security — you get a wide field of view, at the cost of everything looking further away than it is. A concave mirror does both things depending on distance. Outside the focal point it produces a real inverted image, which is how a reflecting telescope works; inside it, a virtual enlarged one, which is how a shaving mirror works.
How the Mirror Equation Calculator works
Image position and size for a concave or convex spherical mirror. The focal length is half the radius of curvature, and the sign of that focal length is what separates the two cases entirely.
Also known as: concave mirror image distance · why do convex mirrors shrink things · focal length from radius of curvature · shaving mirror magnification
Frequently asked questions
What is the mirror equation?
1/f = 1/u + 1/v, identical in form to the thin lens equation. The focal length is half the radius of curvature — positive for concave, negative for convex.
Why do convex mirrors always shrink things?
Because a negative focal length always produces a virtual, upright, reduced image regardless of object distance. That gives a wide field of view, which is why they are used as wing mirrors and for shop security.
How does a shaving mirror magnify?
It is concave, and your face sits inside its focal point. That produces a virtual, upright, enlarged image. Step back past the focal point and the image flips and becomes real.
Why do reflecting telescopes use mirrors?
Mirrors have no chromatic aberration — they bend all colours identically, where a lens does not. They can also be supported from behind, which is why every large telescope built in the last century uses one.
Is the focal length really exactly half the radius?
For paraxial rays close to the axis, yes. Further out, a spherical mirror suffers spherical aberration, which is why serious telescopes use parabolic mirrors instead.
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