# 1.1–1.3 Light: Reflection and Plane Mirrors

F.3 Physics · Topic I Light · Lesson 5

How light travels, the laws of reflection, and the image formed by a plane mirror.

## Figure

Left: angles are measured from the normal, and i = r. Right: extended backwards (dotted lines), the reflected rays meet at the virtual image, and v = u.

## Key points

- **Light** is a form of energy. It travels in straight lines at about $3 \times 10^8$ m s^−1^ and can travel in a vacuum.
- **Light beams ／ 光束** are parallel, divergent or convergent. Rays from distant objects are parallel; rays from nearby objects are divergent.
- **Luminous objects** emit light (the Sun, a working light bulb). **Non-luminous objects** are visible only when they reflect light (the Moon, a chair).
- **Laws of reflection**: the angle of reflection equals the angle of incidence, $i = r$; the incident ray, the **normal ／ 法線** and the reflected ray all lie in the same plane.
- **Regular reflection** (flat, smooth surfaces) gives clear images; **diffuse reflection ／ 漫反射** (rough surfaces) gives no clear image. All reflections obey the laws of reflection.
- **Full-length mirror**: at least half your height, with its bottom edge at half the height of your eyes; your distance from the mirror does not matter.
- **Moving mirror**: if the mirror moves towards or away from a still object at speed $s$, the image moves at $2s$. **Rotating mirror**: with the incident ray fixed, turning the mirror through $x$ turns the reflected ray through $2x$.

## Must know

| Property of the image | Meaning |
|---------|-----------|
| **Virtual ／ 虛像** | no light actually passes through the image, so it cannot be caught on a screen |
| **Erect (upright)** | the right way up |
| **Laterally inverted ／ 橫向倒置** | left and right are swapped |
| **Same size** | the image is as tall as the object |
| **Image distance = object distance** | the image is as far behind the mirror as the object is in front of it ($v = u$) |

If a ray makes an angle $\theta$ with the mirror surface, its angle of incidence is $90^\circ - \theta$.

## Common mistakes

- ✗ A ray strikes a mirror at 35° to its surface: "angle of incidence = 35°". ✓ Angles are measured from the **normal**: $i = 90^\circ - 35^\circ = 55^\circ$, so $r = 55^\circ$.
- ✗ "The Moon is a luminous object." ✓ The Moon is **non-luminous**: moonlight is sunlight reflected by the Moon.
- ✗ "Diffuse reflection does not obey the laws of reflection." ✓ It does; only the normals point in different directions.
- ✗ Ken stands 3 m from a mirror and walks 1 m towards it: "I am 2 m from my image." ✓ 2 m is his distance from the mirror; his image is 2 m behind it, so he is **4 m** from his image.
- ✗ "A virtual image cannot be seen." ✓ It can be seen and photographed; it just cannot be caught on a screen.

## Quick check

1. A light ray makes an angle of 25° with the surface of a plane mirror. Find the angle of incidence and the angle of reflection.
2. State five properties of the image formed by a plane mirror.
3. A girl is 1.6 m tall. What is the minimum length of a plane mirror in which she can see her whole body? Does it change if she steps back?
4. A boy stands 2.5 m in front of a plane mirror. How far is he from his image?
5. The incident ray stays fixed and a plane mirror is turned through 10°. Through what angle does the reflected ray turn?

## Answers

1. $i = 90^\circ - 25^\circ = 65^\circ$, and $r = 65^\circ$.
2. Virtual, erect, laterally inverted, same size as the object, image distance = object distance.
3. 0.8 m, half her height; no, her distance from the mirror does not matter.
4. 5 m: the image is 2.5 m behind the mirror.
5. 20°.

## Did you know?

Apollo astronauts left special mirror panels on the Moon. Scientists still fire lasers at them and time the reflected light to measure the Earth–Moon distance to within a few centimetres.