Why Mirrors Reflect Images

When a ray of light reaches a surface, it may be absorbed, transmitted or reflected. A mirror reflects a large share of visible light. The law of reflection says that the angle at which a ray arrives equals the angle at which it leaves, measured from an imaginary line perpendicular to the surface.

This rule applies to every tiny ray. Light from a lamp strikes your face, then rays from many points on your face travel toward the mirror. The mirror sends some of those rays into your eyes. Your brain uses their directions to judge where the light seems to come from.

A smooth surface keeps nearby rays organised, producing a clear reflection. A rough wall also reflects light, but its uneven surface sends rays in many directions. That scattered reflection lets you see the wall from different positions, but it does not form a sharp image. Polished metal and still water can create reflections for the same reason.

After reflected rays enter your eyes, your brain traces them backward in straight lines. They appear to come from a point behind the mirror. The rays do not actually meet there, so the image is called virtual. You cannot project it onto a screen placed behind the mirror because no light is travelling through that imagined space.

In a flat mirror, the image appears the same distance behind the mirror as the object is in front. It is upright and the same size. Moving closer makes your image seem closer because the apparent position follows your own distance from the mirror.

People often say a mirror reverses left and right. More precisely, it reverses the direction perpendicular to its surface, front and back. Your image raises the hand opposite the one you would expect if you imagined another person turning around to face you. The mirror is not secretly swapping labels. Your comparison is doing most of the mischief.

A simple diagram can make mirror images much easier to understand:

• •Draw a straight line for the mirror.
• •Mark one point on the object.
• •Draw two rays from that point to the mirror.
• •Reflect each ray at an equal angle.
• •Extend the reflected rays backward with dotted lines.

A mirror that curves inwards, like the inside of a spoon, is called concave. It brings reflected rays towards a point called the focus. If you stand close to a concave mirror, inside that focal point, you see an upright, magnified virtual image, which is why make-up and shaving mirrors are shaped this way. Farther away, the rays actually cross and form a real, upside-down image that can be caught on a screen. Large reflecting telescopes use curved mirrors to gather faint light from distant stars in exactly this way.

A mirror that bulges outwards is convex. It spreads reflected rays apart, so the image is always virtual, upright and smaller than the object. That shrinking has a useful side effect: a small mirror can show a wide field of view. Car wing mirrors, shop security mirrors and mirrors placed at blind road corners use this shape. Because the image is reduced, cars in a convex wing mirror look farther away than they really are, which is why some mirrors carry a printed warning that objects are closer than they appear.

Glass on its own reflects only a small share of light, which is why you can see faint reflections in a window. A mirror needs a thin metal coating. For centuries, glassmakers in Venice made mirrors by backing glass with a mixture of tin and mercury, a process that exposed workers to toxic mercury vapour. In the nineteenth century the German chemist Justus von Liebig developed a way of depositing a thin layer of silver on glass through a chemical reaction. Today most household mirrors use silver or aluminium behind the glass.

A so-called one-way mirror is really a partly coated glass that reflects some light and lets some through. It works only because of lighting. The observation room is kept dark while the other room is brightly lit. People in the bright room see mainly their own strong reflection, because very little light comes through from the dark side. If the observation room were lit, people could see straight in. You can sometimes spot such glass by cupping your hands against it to block the reflection and looking through.

Here is a puzzle worth testing: how tall must a flat wall mirror be for you to see your whole body? The answer is half your height, and surprisingly it does not depend on how far away you stand. Light from your feet must reflect into your eyes, and by the angle rule it strikes the mirror at a point halfway between the height of your eyes and the floor. Light from the top of your head meets the mirror halfway between your eyes and your crown. The section between those two points is exactly half your height. Step back and those two points stay at the same heights.

Two mirrors together produce more surprises. Stand between two parallel mirrors and you see a corridor of images stretching away, each one formed by light that has bounced one more time. The distant images grow dimmer and take on a greenish tint, because each pass through the glass and each reflection absorb a little light, and ordinary glass absorbs red and blue slightly more than green. Now join two mirrors at a right angle and look into the corner. The light reflects twice, the two reversals cancel, and you see yourself as other people do, so when you raise your right hand, your image raises its own right hand.

If two mirrors at right angles return light along a reversed path, three mirrors meeting like the inside corner of a box go further. Any ray entering such a corner reflects off all three surfaces and leaves travelling straight back the way it came, whatever angle it arrived at. This device is called a corner reflector or retroreflector. The reflectors on bicycles and road signs contain many tiny moulded corners like this, which is why they shine brightly back towards a car's headlights and the driver behind them, while looking dull to someone standing off to one side.

The same trick works across space. Astronauts on the Apollo 11, 14 and 15 missions left panels of corner reflectors on the Moon, and two Soviet robotic rovers carried them too. Observatories on Earth fire short laser pulses at these panels and time how long the light takes to return, roughly two and a half seconds for the round trip. Only a tiny number of photons make it back from each pulse, yet the timing pins down the Earth to Moon distance to within centimetres or better. The measurements show the Moon drifting away from Earth by about 3.8 centimetres a year.

Mirrors form images by reflecting light according to a predictable angle rule. Your eyes receive the reflected rays, and your brain traces them backward to a virtual position behind the mirror. Follow the rays, and the apparent room behind the glass stops being mysterious.