Mirror Equation Calculator Formula

Understand the math behind the mirror equation calculator. Each variable explained with a worked example.

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Formulas Used

Image Distance

image_distance = 1 / (1/focal_length - 1/object_distance)

Magnification

magnification = -(1 / (1/focal_length - 1/object_distance)) / object_distance

Variables

VariableDescriptionDefault
focal_lengthFocal Length (+ concave, - convex)(cm)20
object_distanceObject Distance(cm)40

How It Works

Mirror Equation

The mirror equation is identical in form to the thin lens equation.

Formula

1/f = 1/d_o + 1/d_i

For a concave mirror, f is positive. For a convex mirror, f is negative. The focal length equals half the radius of curvature: f = R/2.

Worked Example

An object 40 cm from a concave mirror with f = 20 cm.

focal_length = 20object_distance = 40
  1. 011/f = 1/do + 1/di
  2. 021/20 = 1/40 + 1/di
  3. 031/di = 1/20 - 1/40 = 1/40
  4. 04di = 40 cm
  5. 05M = -40/40 = -1 (inverted, same size)

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