Reflection and mirrors

To see your whole body in a flat mirror you need a mirror only half as tall as you are, wherever you stand.

The law of reflection

Throw a ball at a wall at an angle and it bounces off at the same angle on the other side. Light does the same at a smooth surface, and OpenStax states it in one line: the angle of reflection equals the angle of incidence, θr = θi. The angles are measured from the normal, an imaginary line at right angles to the surface at the point where the ray strikes, not from the surface itself. The incoming ray, the reflected ray and the normal all lie in the same flat plane.

Smooth and rough surfaces

If every surface reflected like a mirror, you could see a sheet of paper only from one angle. You can see it from anywhere in the room because its surface is rough on the scale of the wavelength of light. OpenStax explains that parallel rays hitting a rough surface strike tiny facets tilted in many directions, so each obeys the law of reflection but they leave in all directions. This is diffuse reflection, and it is how we see people, clothes, leaves and walls. A mirror is smooth compared with the wavelength, so parallel rays stay parallel after reflection and only an observer in the right place sees the bright reflection. Moonlight on a lake is a mix: the water is shiny but uneven, so the reflection spreads into a long glittering streak.

Images in a flat mirror

When you look into a flat mirror your image seems to stand behind the glass. OpenStax shows why: the rays that reach your eyes leave the mirror as if they came from a point behind it, and the law of reflection puts that point exactly as far behind the mirror as you stand in front of it. The image is the same size as you and upright, but left and right appear swapped. It is a virtual image: no light actually passes through the place where it seems to be, so you cannot catch it on a piece of paper held behind the mirror. A camera can still photograph it, because the camera, like your eye, collects the rays and traces them back.

The half-height rule in the lead comes from the same geometry. Light from your feet must reflect off the mirror at a point halfway between your eyes and your feet to come back up to your eyes, and light from the top of your head reflects halfway between your eyes and the top of your head. So the mirror only has to cover the strip between those two points, half your height, and stepping back does not change that, because the image moves back by the same amount.

Mirrors that send light straight back

Two mirrors at right angles return a ray in the direction it came from, whatever the angle it arrives at. OpenStax calls this a corner reflector. Bicycle and road-sign reflectors are full of tiny corners, which is why they light up in a car’s headlights and send the light back toward the driver. Astronauts left corner reflectors on the Moon, and laser pulses bounced off them are used to measure the Moon’s slowly increasing distance with great precision. A good household mirror reflects more than 90% of the light that falls on it, according to OpenStax; the rest is absorbed.