A Laser Pointer and a Mirror: Verifying the Law of Reflection

Send a beam at a plane mirror and it leaves along a new direction. That direction is not arbitrary: the angle of reflection always equals the angle of incidence, and both rays lie in the same plane as the normal. A small mirror, a laser pointer and a protractor are enough to measure the law for yourself.

The trap in "the angle of reflection equals the angle of incidence" is not the conclusion. It is where you measure the angles from. Get the baseline wrong and every number is wrong — in a consistent, hard-to-spot way.

Safety first (read this before you start)

• Never aim a laser pointer at anyone's eyes, your own included. Never aim it at windows, metal or a phone screen either — the reflection is just as damaging.
• Use the lowest-power red pointer available (classroom pointers under 1 mW). "High-power" pointers sold online have no place in any experiment.
• The safer option is a torch instead of a laser: cut a 2 mm slit in card and hold it in front of the torch to get a flat ribbon of light skimming the paper. It is safe, clearly visible, and works without turning the lights off. For younger students, use this version only.
• A teacher or parent holds the pointer; students draw and measure. Switch it off and put it away the moment you finish.
• Mirror edges can cut. Use a small mirror and tape around its edge.

Materials

• A plane mirror — a pocket mirror is plenty, ideally one that stands up;
• A laser pointer, or a torch and a piece of card with a slit;
• A sheet of white paper, a pencil, a ruler and a protractor;
• Modelling clay or a couple of books to hold the mirror upright;
• For the coplanarity step, a piece of card that can be folded down the middle.

Procedure

1. Draw a line MN across the middle of the paper to mark where the mirror will sit. Choose a point O on it and draw a line perpendicular to MN through O. That perpendicular is the normal; draw it dashed.
2. Stand the mirror on MN with its reflecting face towards your side of the paper, and hold it in place with clay.
3. Aim the beam at O along the surface of the paper, at an angle. Two bright lines appear on the paper: the one going in and the one coming back.
4. Mark two points along the incoming ribbon of light and two along the reflected one. Take the equipment away and join the marks with a ruler to get the incident ray and the reflected ray.
5. With the protractor, measure the angle between the incident ray and the normal, and between the reflected ray and the normal. Record both.
6. Repeat steps 3–5 for two or three different incoming directions, marking fresh points every time rather than drawing from memory.
7. Test coplanarity. Fold a piece of card along the line of the normal and stand it up so one half lies in the plane of the incident ray. Now swing the other half out of that plane — the reflected spot disappears. Only when both halves lie flat in one plane can you see the incident and reflected ribbons at once.

What you should see

Three or four runs typically give something like this:

Run 4 is worth doing deliberately: send the beam in perpendicular to the mirror and it returns along its own path. Both angles are 0° and all three lines coincide. Students often assume this "doesn't count as reflection"; in fact it is a special case of the law, and the cleanest one.

The coplanarity step is persuasive in a way words are not: rotate the card out of the plane and the reflected ribbon vanishes instantly. The reflected ray cannot go wherever it likes — it is confined to the plane set by the incident ray and the normal.

The science: the law of reflection

Collected together, the measurements give the full law of reflection, in three parts:

• The reflected ray, the incident ray and the normal all lie in one plane;
• The reflected ray and the incident ray lie on opposite sides of the normal;
• The angle of reflection equals the angle of incidence.

All three are needed. With only the third, light could emerge from behind the mirror or fly out of the plane of the paper without breaking "the angles are equal". The first two pin down the direction, the third pins down the size, and only together do they fix the reflected ray uniquely.

Reflection has one more important property: the light path is reversible. Send light back along the reflected ray and it returns along the original incident ray. You can check this directly — move the pointer onto the old reflected ribbon, aim at O, and the outgoing beam lands exactly on the old incident ribbon. The everyday version: if you can see another driver's eyes in your mirror, that driver can certainly see yours.

One thing more that must be said plainly: diffuse reflection obeys the law too. Walls, paper and desktops look non-reflective because their surfaces are microscopically rough, so each little patch has its normal pointing a different way and parallel light arrives to be scattered in all directions. Patch by patch, though, the angle of reflection still equals the angle of incidence. Diffuse reflection is why we can see objects that do not emit light at all; and a mirror forms an image precisely because its surface is smooth enough that all those normals point the same way, so parallel light stays parallel after bouncing.

Reflection around us

• The image in a plane mirror sits as far behind the glass as you are in front, laterally reversed — all of it a consequence of this law.
• A periscope uses two parallel mirrors at 45° to the horizontal to walk the light round two right angles and into your eye.
• Car mirrors and corner mirrors use reflection to deliver a view of somewhere you cannot see directly.
• A bicycle rear reflector is a grid of tiny mutually perpendicular faces that send a driver's headlight beam straight back the way it came. It emits nothing and still outshines many lamps.
• Glare on a whiteboard happens when a patch is smooth enough to reflect a window specularly towards a few seats, and only those seats cannot read it. Roughening the surface converts specular reflection back into diffuse reflection.

Five things students get wrong

• Measuring from the mirror. By far the most frequent error here. Angles of incidence and reflection are always measured from the normal. The fix is procedural: draw the normal first, then look for the angle. "Angle of incidence 60°" means 60° from the normal and only 30° from the mirror.
• "The angle of incidence equals the angle of reflection." Backwards. The reflected ray follows from the incident ray, so it is the angle of reflection that equals the angle of incidence. This is not pedantry: with the causation reversed, students imagine that changing the outgoing angle could change the incoming one.
• "Diffuse reflection doesn't obey the law." It does. Every tiny patch of a rough surface satisfies it exactly; the patches simply face different ways, and only the sum looks disorderly. Teach this wrongly and "why can we see things that don't glow?" becomes unanswerable.
• "A plane mirror forms a real image." It does not. No light actually travels behind the glass; the image is where the backward extensions of the reflected rays appear to meet, which makes it virtual. Put a screen behind the mirror and nothing lands on it.
• "A mirror swaps left and right." Strictly, a plane mirror reverses front and back — the direction perpendicular to its surface — not left and right. It feels like a left-right swap because we mentally turn ourselves around a vertical axis to compare. Ask students to raise their right hand and say which hand the image raises, then work out which direction actually got flipped. It makes an excellent discussion.

Teaching notes

• Time and grouping: 30 minutes, pairs. With younger or larger classes, hand out torches and slit cards and no lasers at all.
• Say this before they start: never point the beam at a person or a shiny surface; draw the normal before measuring anything.
• Prep that pays off: print or pre-draw MN and the normal on the sheets. It saves half the time and removes the systematic error from a badly drawn perpendicular.

The step most often skipped. The folded-card coplanarity test gets dropped because "the law already says so". But it is the only moment in the lesson where students watch the light disappear, which convinces far better than reading the statement, and it takes under three minutes.

How to tell they have it. Ask: "A ray meets the mirror at 30° to its surface. What is the angle of reflection?" An answer of 60° means it has landed (30° to the surface is 60° from the normal). An answer of 30° means they are still measuring from the mirror, and the normal needs revisiting.

Take it further

• In the simulator, set the two media to various combinations and watch the grey reflected ray and the red refracted ray appear together and share the energy. Reflection and refraction usually happen at the same time — often one is just too faint to notice.
• Increase the angle of incidence gradually and find the point where the refracted ray vanishes and only reflection remains: total internal reflection. That is how an optical fibre keeps light trapped inside over long distances.
• Build a periscope from two mirrors. Cut a hole at each end of a long box and mount both mirrors at 45°, parallel to each other. Look in the lower hole and you see what is outside the upper one. Set the 45° carefully with a protractor — a small error walks the image straight out of view.
• Count the images in two mirrors. Hinge two mirrors together facing each other and put a coin between them. At 90° you see 3 images, at 60° you see 5, at 45° you see 7. Find the rule linking the angle to the number. (Hint: divide 360° by the angle, then subtract one.)
• At night, shine a torch on a bicycle reflector and on a sheet of white paper, viewing from various positions. The reflector is dazzling only when you stand beside the torch; the paper looks much the same from anywhere. That is retroreflection against diffuse reflection.

When a student's first pencil stroke on a ray-diagram question is the normal rather than the ray, this experiment has done its job.