# Mirror Equation Calculator

Calculate image distance, magnification, and image type for concave and convex mirrors using 1/f = 1/do + 1/di. Free online mirror equation calculator.

## What this calculates

The mirror equation relates the focal length of a curved mirror to the object distance and image distance: 1/f = 1/d_o + 1/d_i. This fundamental formula in geometric optics lets you predict where an image forms, how large it is, and whether it is real or virtual, upright or inverted.

## Inputs

- **Focal Length** (cm) — Positive for concave mirrors, negative for convex mirrors.
- **Object Distance** (cm) — min 0.1 — Distance from the object to the mirror (always positive).

## Outputs

- **Image Distance** (cm) — Positive = real image (in front of mirror), negative = virtual image (behind mirror).
- **Magnification** — Ratio of image height to object height.
- **Image Type** — formatted as text — Whether the image is real or virtual.
- **Image Orientation** — formatted as text — Whether the image is upright or inverted.

## Details

The mirror equation 1/f = 1/do + 1/di applies to both concave and convex mirrors using the sign convention: distances are positive in front of the mirror and negative behind it. A concave mirror has a positive focal length and can produce both real and virtual images, while a convex mirror has a negative focal length and always produces virtual, upright, reduced images.

The magnification m = -di/do tells you the image size relative to the object. When |m| > 1 the image is enlarged; when |m| < 1 it is diminished. A negative magnification means the image is inverted.

Curved mirrors are used everywhere: concave mirrors focus light in telescopes, headlights, and solar furnaces; convex mirrors provide a wide field of view in vehicle side mirrors and security mirrors. Understanding the mirror equation is key to designing any optical system involving curved reflective surfaces.

## Frequently Asked Questions

**Q: What is the difference between a real and virtual image?**

A: A real image is formed where light rays actually converge and can be projected onto a screen (positive image distance). A virtual image is formed where light rays only appear to diverge from and cannot be projected (negative image distance).

**Q: Why do convex mirrors always produce virtual images?**

A: Convex mirrors diverge incoming parallel rays. Since the reflected rays never actually converge, the image always forms behind the mirror (virtual), is always upright, and is always smaller than the object.

**Q: How is the mirror equation different from the thin lens equation?**

A: Mathematically they are identical: 1/f = 1/d_o + 1/d_i. The difference lies in the sign conventions and whether light passes through (lenses) or reflects off (mirrors) the optical element.

**Q: What happens when the object is at the focal point of a concave mirror?**

A: When d_o = f, the mirror equation gives 1/d_i = 0, meaning the image distance is infinity. Reflected rays emerge parallel and never converge, which is the principle behind flashlights and headlights.

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Source: https://vastcalc.com/calculators/physics/mirror-equation
Category: Physics
Last updated: 2026-04-21