Short on time? This page is the recap. For explanations, Figures 1–4 and the worked examples, use the full study guide.
Recap
- A light ray is a straight line at 90° to the wavefronts, pointing the way the wave travels. Plane wavefronts give parallel rays; a point source gives rays pointing outward.
- The ray model (geometric optics) works when the wave nature of light can be ignored. It cannot explain diffraction or interference (Unit 14).
- A laser beam is a single, narrow, one-colour, coherent beam that you can treat as a ray.
- A ray diagram shows the path of light before and after it meets matter. Use a ruler, arrows and a dashed normal.
- Incident ray, normal and reflected ray lie in one plane, with the two rays on opposite sides of the normal.
- Light paths are reversible.
Key relationships
| Relationship | Meaning | Use it to |
|---|---|---|
| θᵢ = θᵣ | angles from the normal | find the direction of a reflected ray |
| angle from normal = 90° − angle from surface | converts a surface angle | avoid the most common angle error |
| angle between incident and reflected rays = 2θᵢ | rays on opposite sides of the normal | find how far apart the beams are |
| mirror turns by φ → reflected ray turns by 2φ | incident ray fixed | optical-lever and rotating-mirror problems |
| spot shift = L tan(2φ) | wall at distance L, met at 90° before the turn | turn an angle into a distance |
| Type of reflection | Surface | Normal over the lit area | Result |
|---|---|---|---|
| Specular | smooth (mirror, still water) | same direction | parallel rays stay parallel; clear image |
| Diffuse | rough (paper, cloth, dry road) | varies from patch to patch | rays scatter in many directions |
Assumptions behind the numbers
- Mirrors are flat over the region where the light lands.
- Objects are much larger than the wavelength of light, so the ray model holds.
- Angles are in degrees.
Mistakes to avoid
- Measuring from the surface. Convert to an angle from the normal first.
- Reflected ray turns by φ. It turns by 2φ.
- “Rough surfaces disobey the law.” Every patch obeys it; the normals differ.
- Rays without arrows, or without a normal drawn at the point of reflection.
- Using rays for diffraction. Spreading through a narrow gap needs the wave model.
Quick self-check
- A ray makes 20° with a mirror surface. What is the angle of reflection? (70°)
- A mirror turns through 6°. The incident ray is fixed. How far does the reflected ray turn? (12°)
- The angle of incidence is 25°. What is the angle between the incident and reflected rays? (50°)
- Why can you read a page from any seat in a room? (Diffuse reflection sends light from each point of the page in all directions.)
Next: practice questions.