Light: Mirrors and Lenses · Lesson 3 of 7
What Are the Laws of Reflection?
“Investigate the rules that connect an incoming light ray with its reflected path.”
• Identify incident rays, reflected rays, the point of incidence, and the normal. • Measure reflection angles from the normal rather than from the mirror. • Use experiments to explain both laws of reflection. • Predict reflection at normal incidence and at a tilted mirror. • Connect historical water-reflection observations to the same reflection principles.
Follow one narrow beam of light
So far we have described images. Now we investigate the light itself. A narrow beam makes it easier to follow a path: shine it toward a mirror and notice the direction in which it comes back. Changing the direction of the incoming beam changes the reflected direction, but the change follows a definite rule.
We represent the path of light using a straight line with an arrow. This representation is a ray. The line shows the path, while the arrow shows the direction of travel. A beam contains light travelling along many paths; using a narrow beam helps us represent its direction with a single ray.
The ray of light that travels toward the mirror and strikes it.
The ray of light that leaves the mirror after reflection.
The point on the mirror where the incident ray strikes the reflecting surface.
Call the point of incidence O. At this point draw an imaginary reference line perpendicular to the reflecting surface. Perpendicular means making a right angle of 90°. This reference line, called the normal, lets us measure the two light-ray angles consistently. It is a construction line, not another light ray.
An imaginary line perpendicular to a reflecting surface at the point of incidence.
Measure two angles using the same reference
The incident and reflected rays each make an angle with the normal. Using the same reference is essential: a measurement from the mirror itself would give a different angle. The normal is perpendicular to the mirror, so an angle with the normal and the corresponding angle with the mirror add up to 90°.
The angle between the incident ray and the normal at the point of incidence. It is represented by i.
The angle between the reflected ray and the normal at the point of incidence. It is represented by r.
Place a white sheet on a table and support a plane mirror upright. Cover the openings of a comb with black paper except for one narrow slit, and support it using a paper clip. Shine a torch through the slit to produce a narrow beam along the sheet. Arrange the beam so it meets the mirror.
- Trace the mirror position and the incident and reflected beam directions using a pencil.
- Remove the mirror and mark O where the traced incident ray meets its position.
- Draw the normal at 90° to the mirror line at O.
- Use a protractor to measure i and r from the normal. Record both angles.
- Repeat with different incident directions, keeping the other apparatus suitable for tracing.
- Finally send the incident beam along the normal and observe its return path.
| Trial | Angle of incidence i | Angle of reflection r |
|---|---|---|
| First direction | Measure from the normal | Measure from the normal |
| Second direction | Change the incident direction and measure | Measure the new reflected direction |
| Third direction | Repeat and record | Repeat and record |
| Along the normal | 0° | 0° |
This table is a recording guide, not a set of measurements that you must obtain. Your actual experimental values may differ slightly because of a broad beam, imperfect alignment, pencil lines, or protractor readings. With careful measurement, the two angles are nearly equal in every trial. The ideal relationship is exact equality.
For example, when the incident ray makes an angle of 30° with the normal, the reflected ray also makes an angle of 30° with the normal, on the other side of it. This rule allows you to predict the outgoing direction instead of guessing it.
Problem
A ray strikes a plane mirror at 35° to the normal. Find the angle of reflection.
- 1.The stated 35° is the angle of incidence because its reference is the normal.
- 2.The first law gives r = i.
- 3.Therefore the angle of reflection is 35°. Draw the outgoing ray on the other side of the normal.
Problem
A reflected ray must be drawn when the incident ray makes 25° with the mirror surface. What is its angle of reflection?
- 1.The 25° is measured from the surface, so it is not i.
- 2.The normal is 90° to the surface. Thus i = 90° − 25° = 65°.
- 3.Use r = i, giving an angle of reflection of 65° from the normal. The reflected ray makes 25° with the mirror.
Problem
A ray is incident at 40° to the normal. What angle does the reflected ray make with the mirror?
- 1.Use the first law to find r = 40° from the normal.
- 2.The mirror and normal form a right angle. Subtract r from 90° to find the angle with the mirror.
- 3.The required angle is 90° − 40° = 50°. Answering 40° would use the wrong reference line.
An angle of 40° with the normal and an angle of 40° with the mirror describe different incident directions. Identify the normal before applying i = r. The angle symbols do not refer to the opening between the two light rays.
All three lines lie in one plane
Equal angles alone are not enough to describe reflection in space. Imagine a ray leaving the mirror in a direction above the drawing paper: it might make the right angle but would not follow the observed path. A second law states that the incident ray, reflected ray, and normal at O all lie in the same plane. A plane is a flat surface or an imaginary flat sheet extending in two directions.
Use the same torch, slit, and mirror arrangement, but let part of a stiff sheet extend beyond the table. Observe the reflected beam on this flat extension. Bend the extension downward at the table edge, then flatten it again, while leaving the mirror and incoming beam unchanged.
The beam is visible along the extended paper when it is flat. When the extension is bent away from the original plane, the reflected beam is no longer traced along that portion. On flattening the paper, the beam appears there again. The paper has moved; the reflected beam has not turned down to follow it. This supports the second law.
The incident ray, the reflected ray, and the normal to the mirror at the point of incidence all lie in the same plane.
The normal is fixed by the mirror surface at O. You can send rays toward that same point from different directions; the normal remains the same if the mirror does not move. For each incident ray, its plane with the normal determines the plane of the reflected ray. Different experiments at the same point need not share one fixed plane for every possible incident direction.
Normal incidence and tilted mirrors
A ray travelling along the normal makes no opening angle with it, so its angle of incidence is 0°. The reflected ray returns along the same line in the opposite direction. Its angle of reflection is also 0°. Reflection still occurs; a zero angle does not mean that the light disappears.
If the mirror is tilted, draw a new normal perpendicular to its tilted surface. Measure from that normal, not from a page edge or a remembered vertical line. A ray that follows this new normal still has i = r = 0°. A ray making 20° with the new normal has an angle of reflection of 20°.
Problem
A tilted mirror receives a ray along its normal. A classmate claims that the angle of incidence must now be 90°. Is that correct?
- 1.Find the normal to the actual tilted mirror, rather than using the page as a reference.
- 2.The incident ray follows this normal, so the angle between them is 0°.
- 3.The reflected ray retraces the line in the opposite direction. Both i and r remain 0°; the mirror’s tilt does not change the rule.
Reflection in scientific observation
The same reflection principles apply to plane and spherical mirrors. Curved surfaces change the local orientation of the normal from point to point, but they do not cancel either law. This becomes important when we investigate many parallel rays in the next lesson.
The source describes astronomers in the time of Bhāskara II, more than 800 years ago, observing reflected stars and planets in shallow bowls of water. Tubes placed at suitable angles helped them measure positions. These methods suggest a practical understanding of reflection, although the source does not claim that their literature explicitly stated the two laws.
Check your understanding
Decide what each angle is measured from before doing a calculation. Then use both laws to describe the direction of the reflected ray.
Quiz
The normal is drawn:
A ray makes 30° with the normal. What is its angle of reflection?
An incident ray makes 20° with the mirror. Its angle of incidence is:
What happens when a ray falls along the normal?
What does the bent-paper investigation show?
When a mirror is tilted, which line should be used to measure i and r?
Practice Problems
- Draw and label an incident ray, reflected ray, normal, point of incidence, mirror, i, and r.
- For i = 15°, 45°, and 70°, find r and the reflected ray’s angle with the mirror.
- A ray makes 65° with a mirror surface. Find its angle of incidence and angle of reflection, explaining each step.
- Draw reflection for a ray along the normal of a horizontal mirror and then for a ray along the normal of a tilted mirror.
- Draw the reflected ray when an incident ray makes 20° with the normal of a tilted mirror. Use a ruler and protractor.
- Describe what changes, and what does not change, when the extended paper is bent in the second-law investigation.
- Explain why observations of celestial objects reflected in water relate to reflection, while avoiding a claim that the historical source explicitly wrote the modern laws.
Key Takeaways
• A ray is a straight-line representation of a light path, with an arrow showing travel direction. • The normal is perpendicular to the reflecting surface at the point of incidence. • The angle of incidence equals the angle of reflection: i = r. • Both reflection angles are measured from the normal, not from the mirror surface. • The incident ray, reflected ray, and normal at the point of incidence lie in one plane. • At normal incidence both angles are 0° and the light reflects back along its incoming line. • The laws apply to plane and spherical mirrors, including tilted arrangements.