# PHYS 2212 Module 13.2

## The Law of Reflection 13.2 The Law of Reflection

### Learning Objectives

By the end of this section, you will be able to:

• Explain the reflection of light from polished and rough surfaces
• Describe the principle and applications of corner reflectors

### Law of Reflection

Reflection of light and other forms of electromagnetic radiation occurs when waves encounter a boundary that does not absorb the radiation’s energy, but instead re-radiates the waves off its surface. In such cases, the incoming light wave is referred to as an incident wave and the wave that is re-radiated from the surface is called the reflected wave. This simple concept can be easily illustrated by a flashlight and a glass mirror.

The law of reflection says that the reflection angle is equal to the incident angle. In equation form, the law of reflection is

In the video below, I explain how to measure the angles, which are always measured from a line drawn normal (perpendicular) to the boundary.

### Specular and Diffuse Reflection

If light reflects off a smooth surface (like a mirror, or a lake), it’s called specular reflection, and it is always true that . If light reflects off a dull surface (like white paper, or a wall), it’s called diffuse reflection, and the light comes out every which way. Microscopically, “dull” means that the surface is not smooth on the scale of the wavelength of light. Of course, microscopically, the reflections are still specular, but the surface is wiggly so the net result is diffuse.

In the figure on the left, the mirror reflects the red, green, and blue components of white light almost equally and the reflected light is the same angle from the normal as the incident light. On the right side of the figure, however, the light that is reflected from the rough surface is scattered in all directions. Also, the rough red surface does not reflect all wavelengths equally because it absorbs most of the blue and green components.

By the way, the “angle of incidence = angle of reflection” rule from a smooth surface (e.g. a shiny metallic surface) arises from Maxwell’s equations. ALL of the classical properties of light ultimately arise from these fundamental underlying equations! Discuss!

Two mirrors make an angle of 115° with each other as illustrated in the figure. A ray is incident on mirror M1 at an angle of 68° to the normal.

Find the direction of the ray after it is reflected from mirror M2 (i.e. What is y2?).