State that for reflection, the angle of incidence is equal to the angle of reflection; recall and use this relationship

Reflection of Light

Learning Objective

State that for reflection, the angle of incidence is equal to the angle of reflection; recall and use this relationship.

Key Definitions

• Incident ray – the incoming ray of light that strikes a surface.
• Reflected ray – the ray that leaves the surface after the incident ray strikes it.
• Normal – an imaginary line drawn perpendicular to the surface at the point of incidence.
• Angle of incidence (\$i\$) – the angle between the incident ray and the normal.
• Angle of reflection (\$r\$) – the angle between the reflected ray and the normal.
• Plane mirror – a smooth, flat reflecting surface.

Law of Reflection

When a ray of light strikes a smooth (plane) surface, the angle it makes with the normal (the angle of incidence) is equal to the angle the reflected ray makes with the normal (the angle of reflection). This can be written as

\$i = r\$

Both angles are measured on opposite sides of the normal.

Diagram

Using the Law of Reflection

1. Identify the point of incidence on the reflecting surface.
2. Draw the normal to the surface at that point.
3. Measure or be given the angle of incidence \$i\$.
4. Apply the law \$i = r\$ to find the angle of reflection \$r\$.
5. Draw the reflected ray making the same angle \$r\$ with the normal on the opposite side.
6. Use the diagram to answer further questions (e.g., position of image, direction of reflected ray).

Common Misconceptions

• Thinking the angles are measured from the surface rather than from the normal.
• Assuming the law applies to rough surfaces; it only holds for smooth (specular) reflections.
• Confusing the incident and reflected rays as being on the same side of the normal.

Worked Example

Question: A ray of light strikes a plane mirror at an angle of incidence of \$30^\circ\$. What is the angle of reflection? Also, if the incident ray makes an angle of \$45^\circ\$ with the mirror surface, what is the angle of incidence?

Solution:

1. Using the law of reflection, \$i = r\$. Therefore the angle of reflection \$r = 30^\circ\$.
2. The angle between the incident ray and the mirror surface is the complement of the angle of incidence:

   \$i = 90^\circ - 45^\circ = 45^\circ.\$

3. Hence the angle of reflection is also \$45^\circ\$.

Practice Questions

1. A light ray strikes a flat mirror at an angle of incidence of \$22^\circ\$. Determine the angle of reflection.
2. If the angle between the incident ray and the mirror surface is \$70^\circ\$, find the angle of incidence and the angle of reflection.
3. In a diagram, the normal to a plane mirror makes a \$15^\circ\$ angle with the reflected ray. What is the angle of incidence?
4. Explain why a plane mirror always produces an image that appears to be the same distance behind the mirror as the object is in front of it, using the law of reflection.

Summary Table

Key Take‑away

For any smooth reflecting surface, the angle of incidence equals the angle of reflection (\$i = r\$). This simple relationship allows you to predict the direction of reflected light, locate images formed by plane mirrors, and solve a wide range of IGCSE physics problems.