Concentrating light with mirrors

Why concave, not convex or flat. The three families of mirrors behave differently when parallel rays strike them. A plane (flat) mirror simply reflects parallel rays back as parallel rays, redirected but not brought together. A convex mirror bulges outward and reflects parallel rays so that they spread apart even more, as if coming from a point behind the mirror. A concave mirror curves inward like the inside of a bowl, and it reflects parallel rays inward, so they converge and cross at (roughly) a single bright spot in front of the mirror. Only this converging behaviour can concentrate light, which is why every device on this page reaches for a concave mirror.

Two directions, one property. The same converging behaviour is used in two opposite ways, and telling them apart is the key skill for this topic:

• Concentrating incoming light. A concave mirror held so it faces the Sun catches the Sun's parallel rays and converges them onto a small, intense bright spot — hot enough, with care, to make paper smoke. Solar cookers and solar furnaces scale this idea up to cook food or generate heat without a flame.
• Gathering and projecting outgoing light. Inside a torch or a vehicle headlight, a small bright bulb sits in front of a concave mirror. Instead of the bulb's light spreading weakly in every direction, the mirror gathers this scattered light and sends it back out as a strong, roughly parallel, forward-directed beam — the reverse of the sunlight-focusing case.

Everyday and scientific devices that rely on this. A dentist's mirror is a small concave mirror held close to a tooth, giving a bright, enlarged, close-up view. A reflecting telescope uses a large concave mirror instead of a lens to gather as much faint starlight as possible from a vast distant object and concentrate it into a bright, clear image — far more light than the unaided eye could ever collect. Historically, the slightly curved, reflecting surface of water held in a shallow bowl served the same purpose for early astronomers, acting as a crude concave mirror centuries before glass mirrors were common.

At this stage the syllabus asks for a qualitative reason, not a ray-diagram construction or a focal-length calculation, so the explanation stays in words and a picture rather than an equation.

Step 1. Picture a bundle of parallel rays — sunlight arriving from so far away that its rays are, for practical purposes, parallel to each other — striking a mirror's surface.

Step 2. Reflection always obeys the same rule at every point on any mirror: the angle at which a ray arrives equals the angle at which it leaves, measured from the surface at that exact point (the law of reflection). What differs between mirror types is simply the shape of the surface at each point, which changes the direction each individual ray is sent off in.

Step 3. On a flat mirror, every point on the surface faces the same direction, so every ray obeys the reflection rule in the same way and the whole bundle stays parallel. On a convex (outward-bulging) mirror, the surface curves away from the incoming rays at every point, so each reflected ray is bent further outward than the last, and the bundle fans apart. On a concave (inward-curving) mirror, the surface curves toward the incoming rays, so each reflected ray is bent inward, and rays that entered side by side are steered to cross each other in front of the mirror.

Step 4. Because every one of those inward-bent rays passes through (roughly) the same small region, the light energy that used to be spread across the whole width of the mirror is now packed into a much smaller area — this is what "concentrating light" means physically: the same total light energy, squeezed into less space, so it is brighter and hotter there. Running the same reasoning in reverse explains the torch and headlight case: light spreading out from a small bulb placed in front of a concave mirror strikes the curved surface at many different angles, and the same inward-bending property sends all of those diverging rays back out travelling in (roughly) the same forward direction, turning a weak, spread-out glow into one strong, directed beam.

Question. A car headlight contains a small bright bulb placed in front of a curved mirror, and a student is also asked to design a simple solar cooker using a mirror and sunlight, without any flame. For each device, state which type of mirror should be used and justify the choice using the idea of concentrating light.

Step 1. Identify what each device actually needs. The headlight needs to take light spreading out weakly from a small bulb and turn it into a strong, forward-directed beam — it needs to gather outgoing light. The solar cooker needs to take the Sun's incoming parallel rays and pack them onto a small area on the food, so heat builds up there — it needs to concentrate incoming light.

Step 2. Rule out the wrong mirrors for both. A plane mirror only redirects light without gathering or concentrating it, so it cannot strengthen a weak beam or focus sunlight to a hot spot. A convex mirror makes any bundle of rays diverge further, which is the opposite of what either device needs.

Step 3. Apply the concave mirror's converging property to the headlight. Placing the bulb at the appropriate position in front of a concave mirror lets the mirror gather the light spreading out from the bulb and send it back out as a strong, roughly parallel, forward beam — exactly what a headlight or torch requires.

Step 4. Apply the same property to the solar cooker. Positioning a concave mirror so it faces the Sun lets it converge the incoming parallel sunlight onto a small area, concentrating enough heat energy there to warm or cook food without any flame — the same converging behaviour, used on incoming rays instead of outgoing ones.

Answer: both devices should use a concave mirror — the headlight to gather and project the bulb's light forward as a beam, and the solar cooker to converge incoming sunlight onto a small hot spot.

Competitive stretch

A reflecting telescope observing a faint, distant galaxy uses the same principle at a much larger scale: a large concave primary mirror gathers a wide column of the galaxy's faint incoming light and converges it to a small, bright image — the bigger the mirror, the more faint light it can collect, which is why professional telescopes use mirrors many metres across rather than small lenses.

• Assuming any curved or shiny mirror concentrates light — only a concave mirror converges parallel rays; a convex mirror diverges them instead.
• Treating torch/headlight reflectors and sunlight-focusing demonstrations as unrelated — both rely on the identical converging property of a concave mirror, just used in opposite directions (gathering outgoing light vs. concentrating incoming light).
• Believing reflecting telescopes use a convex mirror because they observe far-away objects — telescopes use large concave mirrors specifically to gather and concentrate faint incoming starlight.
• Forgetting the safety rule for sunlight-concentrating demonstrations — never look directly at the Sun or at the concentrated bright spot produced by a concave mirror.

Ask the tutor: Want to see how the same concave-mirror idea connects to the images it forms up close, like in a dentist's mirror or a shaving mirror?