Lens & Mirror Equation Calculator
Enter any two of f, u, v and get the third — with magnification, image type and a diagram.
Formula
1/f = 1/u + 1/v
m = −v/u = hi/ho
m = −v/u = hi/ho
Physics behind the lens/mirror equation
The thin-lens equation relates object distance u, image distance v and focal length f for an ideal (paraxial, thin) lens or mirror. A real image forms on the opposite side of the lens and can be projected on a screen; a virtual image forms on the same side as the object and cannot be projected. The sign of v tells you which is which: positive v = real image, negative v = virtual image. Magnification m relates image and object heights.
Worked example
Converging lens, f = 10 cm, u = 30 cm
1/v = 1/10 − 1/30 = 2/30 v = 15 cm (real, inverted) m = −v/u = −0.5 (diminished, inverted) h_i = m·h_o = −1 cm
Related tools
FAQs
What sign convention does this calculator use?
Real-is-positive: u and v are positive against the direction of the incident light. f is positive for a converging lens / concave mirror.
What does negative magnification mean?
The image is inverted. |m| > 1 means enlarged.