PhysicsCalcs
Optics

Mirror Equation Calculator

Calculate focal length, image distance, and magnification for concave and convex mirrors.

Interactive calculator

Mirror Equation Calculator

Calculate image distance, object distance, focal length, and magnification for concave and convex mirrors using 1/f = 1/u + 1/v.

Try an example

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Concave mirror: enter positive f. Convex: enter negative f.
  • Object distance u is positive for real objects.
  • Result shows real/virtual, upright/inverted, and size.

Table of Contents

Key Takeaways

  • Mirror equation: 1/f = 1/u + 1/v, where f = focal length, u = object distance, v = image distance.
  • Concave mirrors have f > 0; convex mirrors have f < 0.
  • v > 0 = real image (in front); v < 0 = virtual image (behind mirror).
  • Magnification m = −v/u: positive = upright, negative = inverted.
  • At u = f (concave), no image forms — rays emerge parallel.

The Mirror Equation

The mirror equation relates object distance, image distance, and focal length for spherical (concave and convex) mirrors under the paraxial approximation. Combined with the magnification equation, it fully characterizes the image formed by any spherical mirror.

Formula & Sign Convention

1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}
m=−vu=hihom = -\frac{v}{u} = \frac{h_i}{h_o}
QuantityPositiveNegative
fConcave mirrorConvex mirror
uReal object (in front)Virtual object
vReal image (in front)Virtual image (behind)
mUpright imageInverted image

Image Formation Cases

Object PositionImageSize
u > 2f (concave)Real, invertedDiminished
u = 2f (concave)Real, invertedSame size
f < u < 2f (concave)Real, invertedEnlarged
u = f (concave)No imageParallel rays
u < f (concave)Virtual, uprightEnlarged
Any u (convex)Virtual, uprightDiminished

How to Use

  1. Choose what to solve for: image distance, object distance, focal length, or radius.
  2. Enter values with correct signs (concave f > 0, convex f < 0).
  3. Click Calculate to get the result with image characterization.

Examples

Shaving mirror (u=10cm, f=15cm)

1/v = 1/15 − 1/10 = −1/30 → v = −30 cm (virtual, upright, 3× magnified)

Concave projector (u=30cm, f=10cm)

1/v = 1/10 − 1/30 = 2/30 → v = 15 cm (real, inverted, 0.5× reduced)

FAQ

What is the difference between the mirror equation and the lens equation?›

They use the same algebraic form (1/f = 1/u + 1/v), but the sign conventions differ. For mirrors, v > 0 means the image is on the same side as the object (real). For lenses, v > 0 means the image is on the opposite side from the object (real).

How do I know if an image is real or virtual?›

Calculate v using the mirror equation. If v > 0, the image is real (light rays actually converge there — can be projected on a screen). If v < 0, the image is virtual (light appears to come from behind the mirror).

What happens when the object is at the focal point?›

When u = f, the equation gives 1/v = 0, meaning v → ∞. No image is formed because reflected rays emerge parallel. This is how flashlights and headlights work — they place the bulb at the focal point.

Do convex mirrors always form virtual images?›

Yes, for real objects. Convex mirrors (f < 0) always produce virtual, upright, diminished images behind the mirror. This is why they are used for wide-angle views (car side mirrors, security mirrors).

Sources

  1. Hecht, E. – Optics (5th ed.)
  2. OpenStax University Physics Vol. 3
  3. The Physics Classroom – Mirror Equation
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

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