Lens and Mirror Calculator
1/f = 1/dₒ + 1/dᵢ, with what the image actually looks like.
1/f = 1/dₒ + 1/dᵢ, with what the image actually looks like.
Positive for converging (convex lens, concave mirror), negative for diverging.
Image distance
15 cm
Real, inverted, reduced — can be projected on a screen
1/f = 1/dₒ + 1/dᵢ. A positive image distance means a real image that can be caught on a screen; a negative one means a virtual image that only exists when you look through the optic. The interesting case is an object inside the focal length of a converging optic. The arithmetic returns a negative image distance, which is not an error. It is a magnifying glass, giving a virtual, upright, enlarged image. Magnification is negative when the image is inverted, which is the convention rather than a sign of trouble. A camera and an eye both form real inverted images; the correction happens in software or in the brain.
How the Lens and Mirror Calculator works
Enter a focal length and object distance for the image position, magnification, and whether the image is real or virtual, upright or inverted. The virtual-image case is not an error. It is what a magnifying glass does.
Also known as: thin lens equation calculator · mirror equation calculator · magnification calculator · image distance calculator
Where to go next
The Lens and Mirror question rarely arrives on its own. These are the ones that usually come with it:
- Snell's Law Calculator — Refraction angle, with the critical angle and TIR.
- Photon Energy Calculator — Energy, wavelength and frequency, from whichever you know.
- Wave Speed Calculator — v = fλ, solved for whichever you are missing.
- Speed Distance Time Calculator — Any one of the three from the other two, in four units.
Frequently asked questions
What is the thin lens equation?
1/f = 1/dₒ + 1/dᵢ. Positive f is converging — a convex lens or a concave mirror. A positive image distance means a real image, negative means virtual.
What is the difference between a real and a virtual image?
A real image can be projected on a screen because the light actually converges there. A virtual image only exists when you look through the optic; the rays merely appear to come from it.
Why does my answer come out negative?
Usually because the object is inside the focal length of a converging lens, which gives a virtual, upright, magnified image. That is not a mistake — it is precisely how a magnifying glass works.
Why is magnification negative?
The sign carries the orientation: negative means inverted. A camera and an eye both form real inverted images, and the correction happens afterwards in software or in the brain.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
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Related calculators
Snell's Law Calculator
Refraction angle, with the critical angle and TIR.
OpenPhoton Energy Calculator
Energy, wavelength and frequency, from whichever you know.
OpenWave Speed Calculator
v = fλ, solved for whichever you are missing.
OpenSpeed Distance Time Calculator
Any one of the three from the other two, in four units.
Open