Wiki / Mirrors / Concave mirror

Concave mirror

Focuses reflected rays with a paraxial focal-length model.

Open in the canvas →

Click the concave mirror to see its live specs and try its parameters — this mini canvas can't be moved, deleted, or added to.

In the real world

A concave (converging) spherical mirror focuses light by reflection the same way a lens focuses it by refraction. For a mirror of radius of curvature R, the paraxial focal length is half the radius, and object and image distances obey the same mirror equation as a lens:

f=R2f = \frac{R}{2}
Paraxial focal length from the radius of curvature.
1f=1do+1di,m=dido\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}, \qquad m = -\frac{d_i}{d_o}
The mirror equation and transverse magnification — identical in form to the thin-lens equation.

That formula is only exact for rays close to the axis. A real sphere brings marginal (off-axis) rays to a focus slightly closer to the mirror than paraxial rays — spherical aberration — which is why fast astronomical mirrors are ground as parabolas instead (see the parabolic mirror page).

In OpticalSetup

OpticalSetup reflects each ray off the mirror's drawn line using the exact vector law of reflection, then applies the same paraxial ray-transfer correction used by the lens element — u' = u − h/f — to the reflected direction. The visible curvature in the icon is cosmetic; the ray/surface interaction happens against the flat line, with focusing added afterward as a per-ray angular correction.

Simplified vs. reality

Because the paraxial correction is applied exactly at every ray height rather than being derived from a real curved surface, this mirror has no spherical aberration at any aperture — every parallel ray converges exactly to the focal point regardless of how far it is from the axis. A real spherical mirror this fast would show visible aberration; this one won't. For a mirror whose curvature is actually ray-traced, see the parabolic mirror.

Related components

Further reading