Lens and Mirror Equation Calculator
Solve thin-lens and spherical-mirror image distances with the real-is-positive Gaussian sign convention stated.
At a glance
- Computes
- Image distance, focal length, or object distance for a thin lens or spherical mirror.
- You supply
- Two of focal length, object distance, and image distance, plus object height.
- Use when
- A single thin lens or spherical mirror, with paraxial rays and one optical axis.
- Assumes
- The real-is-positive Gaussian convention, thin optics, and paraxial rays.
Optics result
Enter two distances
Real-is-positive Gaussian convention.
| Quantity | Value | Unit |
|---|
1 / f = 1 / do + 1 / di; m = -di / do
How?
How this is calculated
The solver uses the real-is-positive Gaussian convention. For mirrors it also reports the signed spherical radius as R = 2f.
Formula: 1 / f = 1 / do + 1 / di; m = -di / do
Magnification
Magnification is image height divided by object height and equals minus image distance divided by object distance. Its sign carries orientation: negative is inverted, positive is upright. Its magnitude carries scale: above one is enlarged and below one is reduced.
A converging lens with focal length 10 cm and an object at 30 cm forms an image at 15 cm, so magnification is -0.5: real, inverted, and half size. Move the object inside the focal length to 5 cm and the image distance becomes -10 cm, so magnification is +2: virtual, upright, and twice size.
A convex mirror with focal length -15 cm and an object at 30 cm gives image distance -10 cm and magnification +0.333: virtual, upright, and reduced. These results use the real-is-positive Gaussian convention and the paraxial thin-lens model. Thick optics, wide-angle rays, and aberrations require a fuller optical model.
Everything on this page is ray optics. A slit is an aperture: it forms no image and has no focal length or magnification, so fringe spacing, interference, and the diffraction envelope belong to the double slit experiment simulator.
Sources
- OpenStax College Physics 2e, Image Formation by Lenses. OpenStax. Retrieved .
- OpenStax College Physics 2e, Image Formation by Mirrors. OpenStax. Retrieved .
Method last reviewed