Skip to content
Hard

The Mirror Formula and Magnification

Simple Explanation

The mirror formula, 1/f = 1/v + 1/u, relates the focal length (f), image distance (v), and object distance (u) for a curved mirror, letting you calculate exactly where an image will form. Magnification, m = −v/u, tells you the image's size relative to the object, and whether it is upright (positive m) or inverted (negative m).

Why Do We Need It?

This formula turns curved-mirror optics from a qualitative sketch into an exact calculation — essential for designing anything from telescopes to dental mirrors to precise specifications.

Formula

The Mirror Equation and Magnification

1/f = 1/v + 1/u; magnification m = −v/u = h(i)/h(o)

The mirror equation relates the distances of the object, the image, and the focal point for a curved mirror. Magnification compares the size of the image to the size of the object, and also reveals whether the image is upright or inverted.

f
— the mirror's focal length, in metres or centimetres (negative for a concave mirror, positive for a convex mirror, using the sign convention where the object side is negative)
u
— object distance from the mirror (always negative, since the object is always in front of the mirror)
v
— image distance from the mirror (negative for a real image in front of the mirror, positive for a virtual image behind it)
m
— magnification (dimensionless) — a negative value means an inverted image, positive means upright; |m| > 1 means enlarged, |m| < 1 means diminished
h(i), h(o)
— image height and object height, in the same units

When to use it: Whenever the image distance, object distance, focal length, or magnification for a curved mirror needs to be found, given the other relevant quantities.

Worked Example

Find the image position and magnification for a concave mirror

A concave mirror has a focal length of 15 cm. An object is placed 30 cm in front of it. Find the image distance and magnification. (Using the sign convention: concave f is negative, object distance u is negative.)

    Why Does This Work?

    This particular result (object at 2f, image also at 2f, magnification exactly −1) is a well-known special case: placing an object at the mirror's centre of curvature (twice the focal length) always produces a real, inverted image of exactly the same size, at the same distance.

    Real-Life Example

    Dentist's mirror

    A dentist uses a small concave mirror held very close to a tooth to see a magnified, upright view.

    By keeping the object (the tooth) closer to the mirror than its focal length, the mirror formula predicts a virtual, upright, MAGNIFIED image — exactly the enlarged view a dentist needs.

    Practice

    A concave mirror has a focal length of 20 cm. An object is placed 50 cm in front of it. Find the image distance v. (Use f = −20 cm, u = −50 cm.)

    Hard
    cm

    Common mistake

    Forgetting to apply the sign convention consistently — mixing positive and negative signs for u, v, and f leads to an image position or magnification with the wrong sign, giving a completely wrong description of the image (real vs. virtual, upright vs. inverted).

    Quick Review

    • 1/f = 1/v + 1/u
    • m = −v/u = h(i)/h(o)
    • Object distance u is always negative; concave f is negative, convex f is positive.
    ← Back to Light