Mirror Formula
Calculate image position and size for concave and convex mirrors.
Essential for mirror design and ray optics problems.
The Formula
1/f = 1/dโ + 1/dแตข 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 |
| dโ | Object distance from the mirror (always positive) |
| dแตข | 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/dแตข
1/dแตข = 1/15 - 1/40 = 8/120 - 3/120 = 5/120
dแตข = 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/dแตข
1/dแตข = -1/20 - 1/10 = -1/20 - 2/20 = -3/20
dแตข = -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