# Law of Reflection The law of reflection states that the angles of an incident ray and reflected ray are the same and the incident ray, reflected ray, and normal are all in the same plane.

The law of reflection states that the angles of an incident ray and reflected ray are the same as each other and are in the same plane as the normal. The law describes the behavior of light reflecting off of a very smooth surface. This is specular reflection or regular reflection. In contrast, diffuse reflection occurs from an irregular surface. The law of reflection is derived from the Fresnel equations.

The law of reflection states that the angle of reflection is the same as the angle of incidence.

### Simple Statement of the Law of Reflection

The law of reflection describes the type of reflection you see from a mirror.

1. The angle between the incident ray and the normal is the same as the angle between the reflected ray and the normal. Another name for the normal is the perpendicular line, with respect to the surface.
2. The incident ray, normal, and reflected ray all lie in the same plane. Changing the direction of the incident ray changes this plane.
3. The incident ray and reflected ray are on opposite sides of the normal. You’ll never see reflected light bounce off a surface on the same side of the perpendicular plane as the incident ray.

While the law of reflection holds true for diffuse reflection, the rough surface produces different combinations of incident/reflected angles, depending on position.

### Law of Reflection Example Problems

For example, what is the angle of reflection if an incident ray strikes a plane mirror with an angle of 30° to the mirror surface?

To answer the question, first find the angle of incidence. Remember, this is the angle between the ray and the normal (not the ray and the surface). Since the normal is 90°, the incident angle is 90 – 30 = 60°. According to the law of reflection, both the incident and reflected angle are the same, with respect to the normal. So, the angle of reflection is 60°.

As another example, find the angle between a reflected ray and the surface if light strikes a mirror with an angle of incidence of 36°.

Knowing the angle of incidence is 36°, you also know the angle of reflection is 36°. However, the question asks about the angle between the reflected ray and the surface. So, subtract the angle of reflection from the normal (90°): 90 – 36 = 54°.

### See It for Yourself

Confirming the law of reflection is easy. You need a mirror, a light source, and a sheet of paper. A small laser pointer works best because it has a tight beam, but you can use any directional light. If you’re using a laser, avoid looking at the beam.

1. Hold the paper so it is perpendicular to the mirror. In other words, one flat edge of the paper sits evenly on the mirror surface.
2. Shine the laser beam along the paper surface, toward the mirror. Observe the angle of the reflected beam on the paper. If you like, trace the path of the light on the paper using a pencil and measure the angles with a protractor.

### Importance of the Law of Reflection

The law of reflection allows the prediction of the path light follows when it strikes a shiny surface. This finds use in mirrors, lenses, cameras, and telescopes. The law of reflection governs how our eyes see images. Cameras also capture reflected light. If many parallel rays strike a mirror surface, only a viewer at a particular angle sees the reflection.

### References

• Fox, Mark (2010). Optical Properties of Solids (2nd ed.). Oxford: Oxford University Press. ISBN 978-0-19-957336-3.
• Lekner, John (1987). Theory of Reflection, of Electromagnetic and Particle Waves. Springer. ISBN 9789024734184.
• Mandelstam, L.I. (1926). “Light Scattering by Inhomogeneous Media”. Zh. Russ. Fiz-Khim. Ova. 58: 381.
• Tan, R.T. (2013). Specularity, Specular Reflectance. In: Ikeuchi K. (eds.) Computer Vision – A Reference Guide. Boston, MA: Springer. ISBN 978-0-387-31439-6. doi:10.1007/978-0-387-31439-6