🔎 Lens & Mirror Equation Calculator
Enter focal length and object distance to find the image distance and magnification — and whether the image is real or virtual, upright or inverted, magnified or reduced.
Image distance dᵢ
30
Magnification m
-2×
Thin-lens / mirror equation: 1/f = 1/dₒ + 1/dᵢ; magnification m = −dᵢ/dₒ. Positive dᵢ = real image; positive m = upright. 🔒 In your browser.
How the lens & mirror equation calculator works
The thin-lens (and mirror) equation is 1/f = 1/dₒ + 1/dᵢ, and the magnification is m = −dᵢ/dₒ. Enter the focal length (positive for a converging lens or concave mirror, negative for diverging/convex) and the object distance; the tool solves for the image distance and magnification and interprets the signs: a positive image distance means a real image, and a positive magnification means an upright image.
The sign convention — and the real-vs-virtual, upright-vs-inverted verdict — is the differentiator and a common source of errors. Follow the on-page sign rules and the tool reports the image nature for you.
Frequently asked questions
What is the thin lens equation?
1/f = 1/dₒ + 1/dᵢ, relating the focal length f, object distance dₒ and image distance dᵢ. The same form works for spherical mirrors.
How do I know if an image is real or virtual?
From the sign of the image distance: positive dᵢ means a real image (on the far side of a lens / in front of a mirror); negative means a virtual image. This tool states which.
What is magnification?
m = −dᵢ/dₒ. Its size is how many times larger the image is; a positive m is upright, a negative m is inverted. |m| > 1 is magnified, |m| < 1 reduced.
What sign do I use for focal length?
Positive for a converging (convex) lens or concave mirror; negative for a diverging (concave) lens or convex mirror. Enter it with the correct sign.
What happens when the object is at the focal point?
The image forms at infinity — the rays leave parallel, so there’s no finite image distance. The tool flags this case.