In Transverse Pulses and Transverse Waves we saw that when a pulse or wave strikes a surface it is reflected. This means that waves bounce off things. Sound waves bounce off walls, light waves bounce off mirrors, radar waves bounce off aeroplanes and it can explain how bats can fly at night and avoid things as thin as telephone wires. The phenomenon of reflection is a very important and useful one.

We will use the following terminology. The incoming light ray is called the incident ray. The light ray moving away from the surface is the reflected ray. The most important characteristic of these rays is their angles in relation to the reflecting surface. These angles are measured with respect to the normal of the surface. The normal is an imaginary line perpendicular to the surface. The angle of incidence, θiθi is measured between the incident ray and the surface normal. The angle of reflection, θrθr is measured between the reflected ray and the surface normal. This is shown in Figure 1.

When a ray of light is reflected, the reflected ray lies in the same plane as the incident ray and the normal. This plane is called the plane of incidence and is shown in Figure 2.

Figure 1: The angles of incidence and reflection are measured with respect to the surface normal.

Figure 2: The plane of incidence is the plane including the incident ray, reflected ray, and the surface normal.

The Law of Reflection states that the angles of incidence and reflection are always equal and that the reflected ray always lies in the plane of incidence.

Definition 1: Law of Reflection

The Law of Reflection states that the angle of incidence is equal to the angle of reflection.

θ i = θ r θ i = θ r

(1)

The simplest example of the law of incidence is if the angle of incidence is 0∘0∘. In this case, the angle of reflection is also 0∘0∘. You see this when you look straight into a mirror.

Figure 3: When a wave strikes a surface at right angles to the surface, then the wave is reflected directly back.

If the angle of incidence is not 0∘0∘, then the angle of reflection is also not 0∘0∘. For example, if a light strikes a surface at 60∘60∘ to the surface normal, then the angle that the reflected ray makes with the surface normal is also 60∘60∘ as shown in Figure 4.

Figure 4: Ray diagram showing angle of incidence and angle of reflection. The Law of Reflection states that when a light ray reflects off a surface, the angle of reflection θrθr is the same as the angle of incidence θiθi.

The Law of Reflection holds for every light ray. Does this mean that when parallel rays approach a surface, the reflected rays will also be parallel? This depends on the texture of the reflecting surface.

Figure 5: Specular and diffuse reflection.

(a) (b)