Table of Contents
Mirror Equation Basics
The mirror equation relates the object distance, image distance, and focal length for spherical mirrors (concave and convex). It predicts where an image will form and its characteristics (real/virtual, upright/inverted, magnified/diminished). This equation is fundamental in optics and is used to design telescopes, headlights, solar concentrators, shaving mirrors, and security mirrors.
Concave mirrors (f > 0) can produce both real and virtual images depending on the object position. They converge light and are used where magnification or focusing is needed. Convex mirrors (f < 0) always produce virtual, upright, diminished images and are used for wide-angle viewing (security mirrors, car side mirrors).
The Mirror Equation
Where f is focal length, do is object distance, di is image distance, m is magnification, hi and ho are image and object heights. Positive di means real image; negative means virtual.
Image Formation Cases (Concave Mirror)
| Object Position | Image Position | Image Type |
|---|---|---|
| Beyond C (do > 2f) | Between F and C | Real, inverted, diminished |
| At C (do = 2f) | At C | Real, inverted, same size |
| Between F and C | Beyond C | Real, inverted, enlarged |
| At F (do = f) | At infinity | No image (parallel rays) |
| Inside F (do < f) | Behind mirror | Virtual, upright, enlarged |
Frequently Asked Questions
What is the sign convention?
In the standard convention: distances are positive on the reflecting side (in front of the mirror). Concave mirrors have positive focal length; convex mirrors have negative focal length. Positive di means real image (in front); negative di means virtual image (behind mirror). Positive magnification means upright; negative means inverted.
What happens when the object is at the focal point?
When do = f, the equation gives di = infinity. Physically, the reflected rays are parallel and never converge to form an image. This is the configuration used in flashlights and headlights: a bulb at the focal point produces a parallel beam of light.
How does a parabolic mirror differ from a spherical one?
Spherical mirrors suffer from spherical aberration: rays far from the axis focus at different points than rays near the axis. Parabolic mirrors focus all parallel rays to a single point regardless of distance from the axis. This makes parabolic mirrors essential for telescopes, satellite dishes, and solar concentrators where precise focusing is required.