KAHIBARO
Table of Contents
Image formation by a plane mirror
A plane mirror is a flat reflecting surface. Unlike curved mirrors, it does not focus or spread light rays in a special way. Its main effect is to produce an image that appears behind the mirror.
When light from an object reaches the mirror, the rays reflect according to the law of reflection. If the reflected rays enter your eyes, your brain traces them backward in straight lines. Because of this backward tracing, the light seems to come from a point behind the mirror. That apparent source is the image.
The image formed by a plane mirror has several important properties. It is upright, it has the same size as the object, and it is as far behind the mirror as the object is in front of it. The image is also virtual, which means light does not actually pass through the image point behind the mirror.
For a plane mirror, the image distance equals the object distance in magnitude:
$$d_i = d_o$$
when measured perpendicularly from the mirror surface on opposite sides.
The image is virtual, upright, and the same size as the object.
Virtual image
To understand a virtual image, imagine standing in front of a mirror. Light leaves your face, strikes the mirror, and reflects into your eyes. The reflected rays are real rays, but they diverge after reflection. Your brain extends those rays backward and concludes that they came from behind the mirror.
This is why you can see an image in a mirror, but you cannot project that image onto a screen placed behind the mirror. There is no actual concentration of light there.
Geometry of image location
The position of the image can be found with simple geometry. Take a point on the object. Draw several rays from that point to the mirror. After reflection, those rays obey the law of reflection. If you extend the reflected rays backward, they intersect at one point behind the mirror. That point is the image of the object point.
Since this works for every point on the object, the whole object forms a complete image behind the mirror.
If the object moves closer to the mirror, the image also moves closer by the same amount. If the object moves farther away, the image moves farther away by the same amount.
Size and orientation
A plane mirror produces an image with magnification equal to 1. That means the image height is equal to the object height.
If $h_i$ is the image height and $h_o$ is the object height, then
$$m = \frac{h_i}{h_o} = 1$$
This positive value means the image is upright relative to the object.
For a plane mirror,
$$m = 1, \qquad h_i = h_o$$
The image is upright, not inverted.
Lateral inversion
Although the image is upright, a plane mirror causes lateral inversion. This means left and right appear reversed. For example, text written normally appears backward in a mirror.
It is important to understand that the mirror does not truly swap left and right as a physical rotation would. Instead, the front to back direction is reversed by reflection, and this creates the familiar left-right reversal in appearance.
Object and image distances
Distances for plane mirrors are measured along a line perpendicular to the mirror surface. If a candle is $2 \, \text{m}$ in front of the mirror, its image appears $2 \, \text{m}$ behind the mirror. The total apparent distance between the candle and its image is then $4 \, \text{m}$.
This simple result is often useful in problems involving people, mirrors, and apparent separations.
| Quantity | Plane mirror result |
|---|---|
| Image type | Virtual |
| Orientation | Upright |
| Size | Same as object |
| Image distance | Equal to object distance |
| Magnification | $1$ |
Seeing yourself in a mirror
A common question is why you can see your whole body in a mirror that is only half your height. The reason is geometric. Rays from the top of your head and from your feet reflect from different points on the mirror into your eyes. The required mirror length is only half your height, provided the mirror is positioned correctly.
This result does not depend on how far you stand from the mirror. Standing farther away changes where the rays hit the mirror, but not the minimum required mirror height.
Practical examples
Plane mirrors are used in bathrooms, dressing rooms, periscopes, and many optical instruments. In all these cases, the important idea is that the mirror redirects light while preserving the apparent size and upright orientation of the image.
Two plane mirrors can also create multiple images if arranged at an angle, but the detailed behavior of multiple reflections belongs to more advanced situations. For a single plane mirror, the essential rule is always the same, the image appears symmetrically behind the mirror.
Key facts for a single plane mirror:
$$d_i = d_o$$
$$h_i = h_o$$
$$m = 1$$
The image is virtual, upright, and laterally inverted.
Summary
A plane mirror forms a virtual image behind the mirror because reflected rays are traced backward by the eye. The image is upright, the same size as the object, and located the same perpendicular distance behind the mirror as the object is in front. This makes plane mirrors the simplest and most direct example of image formation in geometrical optics.