Reflection is what happens when light meets a surface and comes back rather than passing through. It needs nothing beyond the straight-line travel from the last lesson, and it introduces the angle convention every remaining lesson in this module uses, so it is the right place to start. By the end you should be able to state the law of reflection precisely enough to apply it, construct the image a flat mirror produces and say where it sits, and predict what a curved mirror does to a beam.
The normal, and why every angle is measured from it
Before any angle can be quoted, you need a line to measure it against, and the line optics always uses is the normal. Normal here has its geometric sense of perpendicular: the normal at a point on a surface is the line through that point at right angles to the surface. On a flat mirror standing vertically, the normal is horizontal; on a curved mirror it is different at every point, pointing along the direction the surface faces there. Angles of incidence and reflection are measured from the normal, never from the surface itself, and that is a convention rather than a discovery — but it is the convention every diagram, every formula and every item uses.
It matters because the two ways of measuring give different numbers that add to ninety degrees, so mixing them up turns a correct piece of reasoning into a wrong answer. A ray striking a mirror at what looks like a grazing eighty degrees to the surface is at ten degrees to the normal, and it is the ten that goes into the law below. If an item quotes an angle without saying what it is measured from, assume the normal; if it says explicitly "to the surface", subtract from ninety before you use it.
The law of reflection
Send a ray at a smooth surface and two things are true of the ray that comes back. First, the angle it makes with the normal equals the angle the incoming ray made with the normal. Second, the incoming ray, the reflected ray and the normal all lie in the same flat plane — the reflected ray does not skew off sideways. The first part is the one items test, and it is worth noticing how strong a statement it is: the surface does not care how bright the light is, what colour it is, or what the mirror is made of. The angle out equals the angle in, always.
Law of reflection
- angle of incidence — between the incoming ray and the normal, in degrees (°)
- angle of reflection — between the reflected ray and the normal, in degrees (°)
Two consequences follow immediately and both get asked. A ray arriving along the normal itself — straight at the mirror, angle of incidence zero — reflects straight back on itself, because the angle out must also be zero. And a ray arriving at forty-five degrees to the normal leaves at forty-five degrees on the other side of it, so the beam is turned through a right angle in total: forty-five in plus forty-five out. That is why a mirror set at forty-five degrees redirects a horizontal beam vertically, and it is the whole design principle of a periscope.
Smooth surfaces and rough ones
The law of reflection holds at every point of every surface, including a sheet of paper, so it cannot by itself be what separates a mirror from a wall. The difference is flatness on the scale of the light's wavelength. A mirror is smooth enough that neighbouring points have normals pointing the same way, so parallel rays arriving together stay parallel on the way out and the pattern of the light survives — that is regular reflection, and it is what lets you see an image. Paper, matt paint and unpolished metal are rough at that scale, so neighbouring normals point in slightly different directions and parallel rays leave in all directions at once. That is diffuse reflection: no image, but the surface is visible from everywhere, which is how you see almost everything in a lit room.
What a plane mirror does
A plane mirror is simply a flat one. Point at it and you see an image of yourself, and the question worth answering carefully is where that image actually is, because the answer is not on the mirror's surface. Take a single point on the object and draw two rays from it to different points on the mirror. Apply the law of reflection at each, and the two reflected rays leave the mirror spreading apart. Spreading rays never meet, so there is nowhere in front of the mirror where the light genuinely comes together. But your eye and brain judge direction by where rays appear to come from, and if you extend both reflected rays backwards in straight lines, they cross at a single point behind the mirror. That crossing point is the image.
An image formed this way, where no light actually arrives and the rays only appear to come from it, is called a virtual image. The word is doing real work: you cannot catch it on a screen, because there is nothing there to catch. Put a sheet of card behind the mirror at the image position and it stays blank. The contrast is with a real image, where rays genuinely converge and cross, which you will meet in the lens lessons and which does show up on a screen. Every plane mirror image is virtual, without exception.
The geometry of the figure gives the position exactly, and it comes out as clean as it possibly could: the image sits on the perpendicular line through the object, as far behind the mirror as the object is in front.
Plane mirror image position
- object distance — from the object to the mirror, in metres (m)
- image distance — from the mirror to the image, in metres (m)
From that single statement the quantity items actually ask for follows in one step. The object and the image sit on opposite sides of the mirror, so the distance between them is the object distance plus the image distance — and since those are equal, the separation is u + u, which is 2u. The gap between you and your reflection is twice your distance from the glass, not your distance from the glass, and that factor of two is the most reliably exploited slip in this lesson, so it is worth setting down on its own.
Object-to-image separation in a plane mirror
- distance from the object to its image, in metres (m)
- object distance — from the object to the mirror, in metres (m)
- image distance — from the mirror to the image, in metres (m)
The image is also the same size as the object, which surprises people who feel that a mirror across the room shows them smaller. It does not: the image is life-size, and it looks small for the same reason a distant person looks small, namely that it is twice as far away as the glass. And it is laterally inverted — left and right are swapped, which is why text held up to a mirror reads backwards and why an ambulance has its lettering reversed. Top and bottom are not swapped, so the image is upright rather than upside down.
Putting it to work
Curved mirrors
Curving a mirror changes nothing about the law of reflection — it still holds exactly, at every point — but it changes the normals, because a curved surface faces a slightly different direction at each point along it. Parallel rays therefore arrive at different angles of incidence depending on where they strike, and leave in correspondingly different directions, which is how a curved mirror can gather or spread a beam that a flat one would simply turn.
A concave mirror curves away from you, like the inside of a bowl. The normals at the top and bottom of the surface tilt inwards towards the middle, so parallel rays arriving along the axis are all steered towards one region in front of the mirror: a concave mirror converges light, and the point where parallel rays meet is its focus. That is why a shaving or make-up mirror held close gives a magnified upright view, why a reflecting telescope uses one to collect starlight, and why a well-shaped concave mirror in strong sunshine can char paper at its focus.
A convex mirror bulges towards you, like the outside of the same bowl. The normals now tilt outwards, so parallel rays are steered apart: a convex mirror diverges light, and it produces a small, upright, virtual image of everything in front of it. Because it squeezes a wide scene into a small image, it gives a much wider field of view than a flat mirror of the same size — the reason it is used for shop security mirrors, blind corners in car parks and passenger-side wing mirrors. The cost of that wide view is the distortion and the fact that everything looks further away than it is.
Why it matters in aviation
Reflection is put to work on an airfield and managed as a nuisance in the cockpit. Signs, markers and boards alongside taxiways and runways are retroreflective: their surfaces are built to send light back towards whatever illuminated them rather than scattering it evenly, so a marker that is unremarkable from the side of the field appears bright to the crew whose own landing and taxi lights are pointed at it. The light doing the illuminating is the aircraft's own, which is why those markings read well from the flight deck in particular and why they dull as the aircraft turns away.
The same law that makes those markings useful makes glass a problem. Instrument faces, display covers and the windscreen all reflect part of any light falling on them, so a brightly lit cockpit at night puts faint images of the panel and of the crew's own hands into the field of view, sitting apparently outside the aircraft where traffic and ground lights should be. Rain on the windscreen adds further surfaces and further stray images. That is why cockpit and instrument lighting is dimmable, and why instrument faces and glazing are treated to cut down what they return.
What the test asks
Two traps dominate. The first is placing the image on the mirror's surface, or at the object's own distance from you, rather than as far behind the glass as the object is in front — with a follow-up option that halves the object–image separation instead of doubling it. Fix it with the arithmetic of Example 2: 2 metres in front means 2 behind means 4 apart. The second is the pair of curved mirrors: expect an item asking which type gives a wide field of view for a security mirror, with concave offered as the answer. Concave collects and converges; convex spreads and shows you more. And watch for angles quoted from the surface instead of the normal — if a ray is described as striking a mirror at 30° to the surface, the angle of incidence is 60°.