How Mirrors Work (A Mirror Is Just a Very Smooth Wall)

A sheet of white paper reflects about 80% of the light that hits it. A good mirror reflects about 95%. Those numbers are startlingly close — and yet one of them shows you your face and the other shows you nothing at all. The difference isn't how much light bounces. It's how tidily.

The Rule: Angle In Equals Angle Out

Throw a ball at the floor straight down and it comes straight back at you. Throw it at a shallow angle and it skims away at the same shallow angle on the other side. Nobody needs to be taught this — it's how every bouncing thing behaves, and anyone who has played squash or pool has an instinct for it.

Light does exactly the same thing, and the rule has a name: the law of reflection. The angle at which light arrives equals the angle at which it leaves.

One detail: angles are measured from the perpendicular

Physicists measure these angles not from the surface itself but from an imaginary line standing straight up out of it, called the normal. So light arriving 30° away from perpendicular leaves 30° away from perpendicular, on the other side.

It's a bookkeeping choice rather than a physical one, but it matters once surfaces start curving — because on a curved mirror the perpendicular points in a different direction at every point, which is the entire reason curved mirrors do interesting things.

Light is also a better bouncer than a ball. A ball loses energy, deforms, picks up spin, and bounces lower each time. Light does none of that. The angle rule is exact.

Why a Mirror and a Wall Behave Differently

Here's the question that actually needs answering, because a white wall obeys the law of reflection just as faithfully as a mirror does.

The difference is smoothness — and specifically, smoothness compared to the size of a light wave.

Visible light has a wavelength around 550 nanometres. For a surface to behave as a mirror, its bumps must be much smaller than that — flat to within roughly 55 nanometres. To put that in perspective, a human hair is about 70,000 nanometres across, so a mirror is smooth to about one thousandth of the width of a hair.

A sheet of paper is a tangle of fibres with bumps thousands of times larger than a light wave. Every tiny facet is angled differently, so each ray obeys the law of reflection perfectly and heads off somewhere completely different from its neighbour. The light is still there. The arrangement is gone.

Physicists call the tidy version specular reflection and the scattered version diffuse. Slide between them below.

This is worth sitting with, because it inverts the intuition. Reflection isn't a special property that mirrors have and walls lack. Everything you can see is reflecting light at you — that's what seeing is. A mirror is simply a surface flat enough not to jumble the light on the way back out.

And the quantities really are close: roughly 80% for white paper against roughly 95% for a good mirror. If you want to poke at gaps like that, a percentage calculator makes the comparison quick — the point being that a 15-point difference in reflectivity produces an absolutely enormous difference in what you see.

Why Your Reflection Looks Like It's Behind the Glass

Stand a foot from a bathroom mirror and your reflection sits, convincingly, a foot behind it. If the mirror is on a wall, your reflection is inside the wall. Obviously nothing is there. So what are you looking at?

Light from your face travels to the mirror, bounces, and enters your eye. Your visual system then does the only thing it knows how to do: it assumes light travelled in a straight line, and traces each ray backwards along that straight line to find where it must have started.

Those backward extensions all meet at a point behind the mirror. Your brain concludes there's a face there. It's not being fooled by a trick so much as applying a rule that is correct essentially all the time.

Real images and virtual images

This gives us the distinction that runs through all of optics:

• A virtual image is where light only appears to come from. No light actually passes through that point. You cannot catch it on a screen — hold a piece of paper behind a mirror and you get nothing, because there is nothing there.
• A real image is a place where light rays genuinely converge. Put a screen there and the image appears on it. This is how a cinema projector works, and how the image forms on the back of your eye.

A flat mirror only ever produces virtual images. The reflected rays spread apart after bouncing, so they never meet anywhere in front. Only a curved mirror can bend them back together.

A mirror only needs to be half your height

A consequence worth trying. To see yourself head to toe, the mirror needs to be only half your height — and that's true no matter how far away you stand.

It falls out of the angle rule. Light from the top of your head must bounce down into your eye, so it strikes the mirror halfway between your eye level and the top of your head. Light from your feet strikes halfway between your eye and the floor. Everything you can see of yourself occupies half the vertical space. Stepping back doesn't help, because you and your image retreat together.

And the classic puzzle: why do mirrors reverse left and right, but not up and down?

They don't. That's the answer — the premise is wrong.

A mirror reverses front and back, along the direction pointing into the glass. Your reflection's nose sticks out toward you where yours sticks out toward it.

The confusion comes from what you do next: you imagine walking round to stand where your reflection is, which means mentally rotating yourself through a half-turn. That rotation is what swaps left and right — and it's your doing, not the mirror's. The giveaway is that you naturally rotate about a vertical axis, because that's how people turn round. Lie on your side in front of a mirror and the "reversal" obligingly becomes an up-down one.

Flat, Concave and Convex

Curve the mirror and the perpendicular points a different way at every point, so parallel rays no longer stay parallel. Two options: curve it inward or outward.

The magnifying mirror

A typical make-up mirror curves inward with a focal length around 20 cm. Bring your face to 10 cm — closer than that focal length — and it produces a virtual image 20 cm behind the glass, upright and twice life size.

Now walk backwards past the focal point and something odd happens: the image flips upside down and becomes real. Try it with a shaving mirror or the back of a spoon. At arm's length you're upside down, and there's a distance in between where the image dissolves entirely, because the rays are momentarily parallel and converge nowhere at all.

The car mirror that shrinks everything

A convex wing mirror does the opposite: it spreads rays out, capturing a much wider slice of the road at the cost of making everything in it smaller. For a typical wing mirror, a car 10 metres behind you appears about 11 times smaller than life size.

Which is the entire reason for the warning etched into it. Your brain estimates distance partly from apparent size, so a car rendered eleven times too small reads as much further away than it is. Objects in mirror really are closer than they appear — the mirror is trading accurate distance judgement for a wider field of view and fewer blind spots, and the manufacturer is legally obliged to warn you about the trade.

The arithmetic behind both cases is the mirror equation. To see it happen — the image distance and magnification for any focal length and object distance, and the rays themselves crossing and the image flipping from virtual to real as you move the object past the focal point — a concave and convex mirror simulator is the clearer way in, since that flip is much easier to watch than to read.

The Takeaway

Mirrors don't do anything exotic. They obey the same bouncing rule as a squash ball, and the same rule as every other surface in the room. What makes them special is negative: they are smooth enough not to ruin the arrangement of the light.

Everything else follows from that plus one habit of your visual system. Your brain insists on tracing light backwards in straight lines, so it places an image behind the glass where nothing exists. Bend the glass inward and the rays converge, making things larger or turning them upside down. Bend it outward and they spread, shrinking the world to fit more of it in.

See the rays for yourself

Move the object past the focal point and watch the image flip from virtual to real, on both concave and convex mirrors. Free, no sign-up, runs in your browser.