Mirror Formula
Reference for the mirror formula 1/f = 1/v + 1/u.
Calculates image position and magnification for concave and convex mirrors, real and virtual images.
The Formula
1/f = 1/dₒ + 1/dᵢ where f = R/2
The mirror formula is identical in form to the thin lens formula. The focal length equals half the radius of curvature of the mirror.
Variables
| Symbol | Meaning |
|---|---|
| f | Focal length (positive for concave, negative for convex) |
| R | Radius of curvature of the mirror |
| dₒ | Object distance from the mirror (always positive) |
| dᵢ | Image distance from the mirror (positive = real, negative = virtual) |
Example 1
An object is 40 cm from a concave mirror with R = 30 cm. Where is the image?
f = R/2 = 30/2 = 15 cm
1/15 = 1/40 + 1/dᵢ
1/dᵢ = 1/15 - 1/40 = 8/120 - 3/120 = 5/120
dᵢ = 24 cm (real image, in front of the mirror)
Example 2
An object is 10 cm from a convex mirror with f = -20 cm. Where is the image?
1/(-20) = 1/10 + 1/dᵢ
1/dᵢ = -1/20 - 1/10 = -1/20 - 2/20 = -3/20
dᵢ = -6.67 cm (virtual image, behind the mirror)
When to Use It
Use the mirror formula when:
- Designing telescopes, headlights, or satellite dishes
- Finding where an image forms in a curved mirror
- Determining image characteristics (real vs virtual, upright vs inverted)
- Calculating the radius of curvature needed for a specific application
Key Notes
- Mirror formula: 1/f = 1/v + 1/u: f is the focal length, v is the image distance, and u is the object distance. All measured from the mirror's pole. The focal length of a spherical mirror is half the radius of curvature: f = R/2.
- Sign convention (real-is-positive): Distances measured in the direction of incident light are positive. For a concave mirror, f is positive; for a convex mirror, f is negative. A real image has positive v; a virtual image has negative v.
- Concave vs convex mirrors: A concave (converging) mirror can form real, inverted images when the object is beyond the focal point, or virtual, upright, magnified images when inside the focal point. A convex (diverging) mirror always produces virtual, upright, diminished images.
- Magnification: m = −v/u: A negative m means the image is inverted. |m| > 1 is magnified; |m| < 1 is diminished. Bathroom mirrors (plane mirrors) have m = +1 — same size, upright, virtual image.
- Applications: Concave mirrors are used in reflecting telescopes, solar concentrators, and dentist mirrors (object inside focal length → magnified upright image). Convex mirrors are used as car rear-view mirrors and security mirrors for their wide field of view.