Light: Mirrors and Lenses · Lesson 4 of 7
How Mirrors Converge and Diverge Light
“See how curved mirrors gather or spread light and connect this behaviour to solar heating.”
• Compare parallel beams reflected by plane, concave, and convex mirrors. • Explain convergence and divergence in everyday language. • Recognise that each reflected ray still follows the laws of reflection. • Explain why concentrated sunlight can produce strong heating. • Connect solar concentrators with cooking, steam production, and electricity generation.
From one ray to a group of rays
The reflection laws describe what happens at each point where light meets a mirror. A beam contains many rays, so a mirror’s overall effect depends on how its surface faces those rays at different points. Comparing several incoming parallel rays makes this difference visible. Parallel rays travel in the same direction without getting closer together or farther apart before reaching the mirror.
A plane mirror has a flat surface, so its normal has the same direction at different points. Identical incoming directions therefore give identical reflected directions. A curved mirror has different local surface directions, and hence different normals, at different points. Each ray still obeys i = r, but the outgoing directions need not all be the same.
Compare three mirrors using a comb and torch
The comb can now produce several narrow beams rather than only one. Keeping many openings uncovered lets us compare the paths side by side. We are investigating changes in beam direction, not the image of a toy. Record the whole pattern instead of judging a single reflected line.
Collect a plane mirror, a concave mirror, a convex mirror, supports, a torch, a comb, a paper clip, and white paper. Use the earlier tracing arrangement, leaving several neighbouring comb openings uncovered. Adjust the setup so the narrow incoming beams are approximately parallel.
- Let the beams fall on the plane mirror and observe the directions of the reflected beams.
- Replace it with the concave mirror and observe whether the reflected beams draw closer together.
- Repeat with the convex mirror and observe whether the reflected beams spread apart.
- Draw arrows showing travel toward the mirrors and away from them. Describe each pattern using your own observations.
The coming together of light rays or beams as they travel. Converging rays become closer to one another.
The spreading apart of light rays or beams as they travel. Diverging rays become farther from one another.
For a plane mirror, parallel incoming rays remain parallel after reflection. Their direction may change, but their paths remain mutually parallel. For a concave mirror, suitable parallel incoming beams reflect toward one another. For a convex mirror, the reflected beams spread apart. This is why concave and convex mirror surfaces have opposite effects on a parallel beam.
| Mirror | Effect on initially parallel rays | What to look for |
|---|---|---|
| Plane | Reflected rays remain parallel | Direction changes without a converging or diverging pattern |
| Concave | Reflected rays converge | They travel toward one another |
| Convex | Reflected rays diverge | They spread apart after reflection |
Do not explain convergence by saying that concave mirrors break the reflection laws. The local normal changes from point to point on a curved surface. Every reflected ray obeys the same laws, and together the rays form a converging or diverging pattern.
Problem
After reflection from a mirror, three beams have a new direction but remain equally separated. Has the mirror converged them?
- 1.Convergence means that the rays move closer together as they travel.
- 2.A direction change alone does not establish convergence.
- 3.Because these beams remain parallel, the observation is consistent with a plane mirror rather than the converging pattern of a concave mirror.
Problem
Several parallel beams approach a mirror and spread apart after reflection. Which spherical mirror fits?
- 1.The important observation is the separation of the reflected beams, not the separation of the incoming beams.
- 2.Spreading reflected beams show divergence.
- 3.A convex mirror produces this pattern for initially parallel incident beams.
Concentrated sunlight can produce heat
Sunlight arriving at a small mirror can be treated as approximately parallel because the Sun is very distant. A concave mirror can gather this light into a small bright region. The light arriving over a larger area is redirected into a smaller area, so that small region receives much more energy than it would from the same sunlight falling directly on it. A surface that absorbs the light becomes hot.
This explains the source’s demonstration with a concave mirror and thin paper. By adjusting the paper’s distance, the reflected sunlight can form a small sharp spot. If enough energy is absorbed, the paper may smoke or ignite. Merely seeing a broad bright patch is not the same as concentrating the light into the smallest useful region.
This is a teacher- or adult-supervised demonstration, not an unsupervised activity. Never look at the Sun or into a mirror reflecting it. Never direct reflected sunlight toward a face or eyes. The source demonstration can ignite paper, so it requires a controlled, suitable location and precautions against fire.
With an adult managing the setup, observe a concave mirror directing sunlight onto thin paper. The adult adjusts the paper position to make a sharp bright spot and holds the arrangement steady only as appropriate. Record how spot size and heating change. You can also study a demonstration video instead of attempting ignition.
Problem
An adult obtains a broad illuminated patch on paper, then a smaller sharp patch using the same concave mirror. Which arrangement is likely to heat the small region more strongly?
- 1.Both arrangements receive sunlight collected by the mirror.
- 2.In the sharp spot, much of that collected light falls on a smaller area.
- 3.The energy is more concentrated there, so heating of that small region is stronger. Keep all safety precautions in place.
Solar concentrators and useful heating
A solar concentrator is a device that gathers sunlight into a relatively small area using mirrors or lenses. It does not create extra energy: it redirects the sunlight that reaches it. A useful design places an absorbing receiver where the redirected light gathers, allowing the received energy to heat a substance.
A device that uses mirrors or lenses to concentrate sunlight onto a relatively small receiving area for useful heating.
In one arrangement, concentrated sunlight heats a liquid to produce steam. The steam can be used in an electricity-generating system, or the heat can be used directly. Other applications include large-scale cooking and solar furnaces. The source notes that sufficiently powerful solar furnaces can even melt steel. These are engineered systems, not a result to expect from a small classroom mirror.
The sequence matters: sunlight is collected, redirected toward a receiver, absorbed, and converted into heating. That heat can then support cooking or another process. This connects the optical behaviour of a concave surface with a practical energy application. In suitable places, solar cooking can reduce the need for electricity or fuel, although its usefulness depends on available sunlight and the design.
Prepare a proposal for a school or home solar cooker that uses mirrors to concentrate sunlight. Include a labelled sketch, the position of the cooking vessel or receiver, a materials list, an estimated local budget, how the device will be aimed, and safety arrangements. Explain how convergence contributes to heating and how weather or changing sunlight may limit use. Keep construction or testing under knowledgeable adult supervision.
Check your understanding
For each question, follow the sequence from surface shape to outgoing light paths and then to the practical effect. Avoid assuming that every curved surface concentrates light.
Quiz
Parallel rays reflected by a plane mirror:
Which mirror makes suitable parallel incident beams converge?
Why can rays reflect in different directions at different points on a curved mirror?
Why can a small bright spot become hot under concentrated sunlight?
Which sequence correctly describes a solar heating system?
Which practice follows the sunlight-demonstration instructions?
Practice Problems
- Draw the broad reflected-beam patterns for plane, concave, and convex mirrors, with direction arrows.
- Explain how different reflected directions can still obey i = r at every point on a spherical mirror.
- Distinguish a changed beam direction from convergence using a plane-mirror example.
- Explain why a small sharp sunlight spot heats paper more strongly than a broad patch, and state the source’s essential safety precautions.
- Trace the stages from sunlight to steam in a solar concentrator and give two uses of the resulting heat.
- Prepare the solar-cooker proposal described above, including the design reasoning and estimated budget.
Key Takeaways
• Parallel rays remain parallel after reflection by a plane mirror. • A concave mirror brings suitable parallel rays together; a convex mirror spreads them apart. • The local normals change across a curved mirror, while each ray still follows both reflection laws. • Concentrating sunlight gathers incoming energy into a smaller region and can cause strong heating. • Solar concentrators can provide heat for cooking, steam production, electricity generation, and furnaces. • Sunlight-concentration demonstrations require adult supervision and protection of eyes, people, and surroundings.