Boneyard Tools

Mirror Equation Calculator

Enter a focal length or radius of curvature plus one distance, or two distances, to solve the mirror equation 1/f = 1/do + 1/di with the magnification and image type.

How to use the mirror equation calculator

  1. Enter the focal length or the radius of curvature (f = R/2), then one distance.
  2. Or leave focal length blank and enter both the object and image distances.
  3. Read the solved values, the magnification and whether the image is real or virtual.

Examples

Concave mirror, distant object

f = 10 cm (R = 20 cm), object distance do = 30 cm
image distance di = 15 cm, magnification = -0.5 (real, inverted)

From radius of curvature

R = 20 cm, object distance do = 30 cm
focal length f = 10 cm, image distance di = 15 cm

Frequently asked questions

What is the mirror equation?

For a spherical mirror, 1/f = 1/do + 1/di, where f is the focal length, do the object distance and di the image distance.

How are focal length and radius of curvature related?

The focal length is half the radius of curvature, f = R/2. You can enter either one and the calculator finds the other.

What sign convention does this use?

Real is positive. A concave (converging) mirror has a positive focal length and radius; a convex (diverging) mirror has negative values. A real image in front of the mirror has a positive image distance.

How is magnification calculated?

Magnification m = -di / do. Negative means the image is inverted, positive means upright, and the absolute value is the size ratio.

What inputs do I need?

Provide a focal length or radius plus one distance, or provide both distances. Distances of zero are not allowed.

Related tools