Slanting in, slanting out: the two angles stay equal. Like a ball rolled at a wall at an angle.
- Angle of incidence
- 35°
- Angle of reflection
- 35°
- The light turns by
- 110°
What’s happening
Throw a ball at a wall and it bounces off in a way you can guess. Light does the same when it hits a mirror. Imagine a line standing straight up from the mirror where the light lands, like a flagpole on flat ground: the normal. The light comes in at some angle to that line, the angle of incidence, and always leaves at the same angle on the other side, the angle of reflection. However steep or shallow you aim it, the two are equal. That is the law of reflection.
Try this
- Where must the torch be for the light to come straight back to it?
- Aim the light so it only just grazes the mirror. Where does it go?
- Keep the torch still and tilt the mirror a little. How far does the light that leaves swing?
- Can you make the two angles different? Try as hard as you like!
- At home: lay a small mirror on the floor and find where you must stand to see the top of a door in it. Then ask a friend to find the spot where they can see your eyes.
Learn more: the law in symbols, three reasons for equal angles, and mirrors left on the Moon
Scientists write the angle of incidence as and the angle of reflection as (θ is the Greek letter “theta”), both measured from the normal. The law says:
So the light turns by what is left of a straight line (180°) once both angles are taken away:
Tilt the mirror and the normal tilts with it. With the torch held still, the angle of incidence changes by the tilt, and so does the angle of reflection, on the other side: the light that leaves swings by twice the tilt. A small wobble of a mirror makes a big sweep of its light, which is how sun signals can be flashed across a valley.
Why equal angles? Three ways of seeing it:
- Like a bouncing ball: the mirror can only push straight back out, along the normal. So the light’s motion along the mirror carries on unchanged, and only its motion into the mirror turns round. That gives equal angles, just as for a ball bouncing off a smooth wall.
- The shortest path: of all the ways to go from the torch to the mirror and on to your eye, the one with equal angles is the shortest, and light takes the quickest path. Heron of Alexandria worked this out nearly 2,000 years ago.
- Light as a wave: every spot on the mirror sends out tiny ripples as the wave arrives. They add up in step in only one direction, the one with equal angles, and cancel out everywhere else.
Why can you see yourself in a mirror but not in a sheet of paper? Paper obeys the same law, but its surface is rough, full of tiny bumps facing every way, so each bit of light bounces off in a different direction and the picture is lost. A mirror is so smooth that light from each point of you comes back together, as an image as far behind the mirror as you are in front of it.
- Periscopes: two mirrors at 45° bend light twice, so you can see over a wall or out of a submarine.
- Bicycle reflectors and cat’s eyes: mirrors at right angles to each other send light straight back to where it came from, to the driver’s eyes. Astronauts left reflectors like this on the Moon, and scientists still bounce lasers off them.
- Curved mirrors: a make-up mirror or a telescope mirror is like many tiny flat mirrors at slightly different tilts, each obeying the same law.