🔎 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.
Worked example: a converging lens
An object 30 cm from a converging lens of focal length 10 cm: 1/dᵢ = 1/10 − 1/30 = 1/15, so dᵢ = 15 cm (a real image) and m = −15/30 = −0.5 (inverted, half size).
Do lenses and mirrors use the same equation?
Yes, the thin-lens equation 1/f = 1/dₒ + 1/dᵢ and magnification m = −dᵢ/dₒ apply to both, provided you follow the sign convention for the focal length (positive for converging lenses and concave mirrors).