Image Formation in Plane Mirrors
A plane mirror forms a virtual, upright image of the same size as the object, located as far behind the mirror as the object is in front of it, and laterally inverted (left and right reversed). In brief: the image cannot be projected on a screen, because the rays only appear to come from it. To see yourself fully in a plane mirror, the mirror needs to be only half your height. Two mirrors at an angle θ produce 360° ÷ θ − 1 images.
The mirror in a bathroom shows an image that seems to be behind the glass. This guide explains how images form in plane mirrors using ray diagrams, lists the properties of the image, covers multiple mirrors and periscopes, compares real and virtual images in a table, works through calculations and corrects common mistakes.
How is an image formed?
Consider a point object O in front of a plane mirror. Rays spread out from O and strike the mirror. Each ray is reflected according to the law of reflection (i = r). Our eye receives the reflected rays, and the brain assumes that light has traveled in straight lines, so the rays appear to diverge from a point I behind the mirror. This point is the virtual image. To draw it, take two rays from O, draw the reflected rays, and extend them backward behind the mirror as dashed lines; they meet at I. By geometry (congruent triangles), the image I is on the line through O perpendicular to the mirror, at the same distance behind the mirror as O is in front.
What are the properties of the image?
- Virtual: it is formed by extended (apparent) rays, not by rays that actually meet, so it cannot be captured on a screen.
- Upright (same orientation as the object).
- Same size as the object (magnification = 1).
- Same distance behind the mirror as the object is in front: image distance = object distance.
- Laterally inverted: left and right are interchanged, as in a mirror image of writing, and this is why AMBULANCE is written reversed on the front of ambulances, so that it can be read in a driver’s rear-view mirror. (Strictly, the image is reversed front to back, which looks like a left-right reversal.)
Moving the object toward the mirror at a speed v makes the image approach at v as well, so the relative speed of object and image is 2v. If the mirror is moved away from a fixed object by d, the image moves by 2d.
What happens with two mirrors?
Two plane mirrors at an angle θ to each other form several images, because the image in one mirror acts as an object for the other. The number of images is N = (360° ÷ θ) − 1 when 360° ÷ θ is an integer. At 90°, there are 3 images, at 60° there are 5, and for parallel mirrors (θ = 0) there is an infinite series of images, as in a barber shop. A periscope uses two parallel mirrors set at 45° to the tube to look over obstacles, and a corner reflector (three mirrors at right angles) sends light back in the direction it came from, as used in bicycle reflectors and the retroreflectors left on the Moon. A kaleidoscope uses two mirrors at a small angle to give a symmetrical pattern.
Real and virtual images compared
| Feature | Real image | Virtual image (plane mirror) |
|---|---|---|
| Rays | Actually meet at the image | Only appear to meet (extended backward) |
| On a screen? | Yes | No |
| Orientation | Usually inverted | Upright |
| Location | In front of the mirror or lens | Behind the mirror |
| Example | Cinema projector image, pinhole camera | Image in a bathroom mirror |
Worked example: distances and mirror height
- Distance to the image. A person stands 2.0 m from a plane mirror. The image is 2.0 m behind the mirror, so the distance between the person and the image is 4.0 m.
- Walking toward the mirror. If the person walks toward the mirror at 1.0 m/s, the image approaches at 1.0 m/s too, so the person approaches the image at 2.0 m/s. After 1.0 s, the person is 1.0 m from the mirror, and the distance between the person and the image is 2.0 m.
- Mirror height. A person 1.70 m tall with the eyes at 1.60 m above the floor wants to see the full body. The ray from the top of the head (1.70 m) reflects at a point halfway between the head and eyes: at (1.70 + 1.60) ÷ 2 = 1.65 m. The ray from the feet (0) reflects at a point at 1.60 ÷ 2 = 0.80 m. The mirror must extend from 0.80 m to 1.65 m, so a height of 0.85 m, half the height of the person, is needed. This does not depend on the distance from the mirror.
- Number of images. Two mirrors at 60°: N = 360 ÷ 60 − 1 = 5 images. At 45°: N = 360 ÷ 45 − 1 = 7 images.
- Rotating the mirror. A ray hits a mirror at normal incidence and is reflected straight back. If the mirror is rotated by 15°, the reflected ray turns through 30°.
How have mirrors been used?
The earliest mirrors were polished obsidian and metal, from about 6000 BCE in Anatolia. Glass mirrors with a metallic backing were made in Venice in the 16th century, and Justus von Liebig developed the silvering process in 1835. Mirrors are used in telescopes, periscopes, solar concentrators and lasers. Hero of Alexandria wrote about mirrors in the first century CE.
Which mistakes are common?
Mistake 1: Thinking that the image is on the surface of the mirror
It is behind the mirror, at a distance equal to the object distance.
Mistake 2: Saying that mirrors reverse left and right
They reverse front and back. The left-right reversal comes from how we compare the image with the object by turning around.
Mistake 3: Believing that you need a mirror of your full height
Half of the height is enough, at any distance.
Mistake 4: Drawing the image rays as solid lines behind the mirror
Extended rays behind the mirror are drawn as dashed lines, as light does not actually go there.