Mirror Equation Calculator
Solve the mirror equation for image distance and magnification of a spherical mirror from its focal length and object distance.
How it works
1 ÷ f = 1 ÷ dₒ + 1 ÷ dᵢ · m = −dᵢ ÷ dₒ
The mirror equation relates focal length, object distance and image distance for a spherical mirror, using the sign convention that a concave mirror has a positive focal length and a convex mirror a negative one. Solving for dᵢ tells you where the image forms; a positive result is a real image in front of the mirror, a negative one a virtual image behind it. The magnification m = −dᵢ/dₒ then gives its size and orientation.
Worked example
A concave mirror with f = 0.20 m has an object at dₒ = 0.50 m. 1/dᵢ = 1/0.20 − 1/0.50 = 5 − 2 = 3, so dᵢ = 1/3 ≈ 0.333 m. Magnification m = −0.333/0.50 ≈ −0.667 — a real, inverted image about two-thirds the object size.
Sources: Curved mirror — Wikipedia
Frequently asked questions
What sign should the focal length have?
Concave (converging) mirrors take a positive focal length; convex (diverging) mirrors take a negative one. The focal length is half the radius of curvature.
What happens when the object is at the focal point?
The reflected rays come out parallel and never meet, so no image forms (the image distance is infinite). This calculator flags that case instead of returning infinity.
Real versus virtual image — how do I tell?
A positive image distance means a real image that could be projected onto a screen in front of the mirror; a negative image distance means a virtual image that appears behind the mirror, like your reflection in a bathroom mirror.
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This calculator is for educational purposes. Double-check important results before acting on them.