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# Geometrical Optics Study Guide

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Updated on Sep 27, 2011

## Introduction

This lesson introduces you to the concept of optics and the geometrical analysis of optical phenomena. We will study the concept of light rays, the laws of reflection, the laws of refraction, and the total internal reflection.

## Light Rays

The study of light encompasses many fields of physics, from mechanics to quantum mechanics and from classical to modern physics. Isaac Newton explained reflection and refraction phenomena based on particle motion, and Max Planck's particle theory explained radiation. On the other hand, the theories of electricity, magnetism, and waves explained light behavior as a wave, as Christian Huygens and James Maxwell did in their theories. A dual explanation of the properties and processes in which light is involved emerged through history. In this lesson, we will address the particle explanation of light.

The geometrical analysis of light propagation assumes that light travels in a straight line through a medium and between two points. If the optical properties of the medium change, light changes the path of propagation. This is called geometrical optics and the propagation of light in a straight line is called ray approximation.

## Reflection of Light

At the boundary between two media, the light ray will change its direction of propagation depending on the properties of the second medium and on the relative position of the light with respect to the surface of the interface. The light propagating from a source toward a smooth surface will bounce from the surface and return to the medium that contains the source. This phenomenon is called reflection of light, the incoming light ray is called the incident ray, and the returning light ray is called the reflected ray. A diagram of the propagation of light at the interface between two media also defines the important angles we will use to set the laws of reflection: the incident and reflection angles. Both angles are defined relative to the perpendicular to the interface called the normal. The two media are shown differently in Figure 18.1 to enhance the surface of separation where reflection occurs.

Experimental work shows that reflection is governed by the following laws:

• The incident, reflected ray, and the normal are in the same plane.
• The angle of incidence and the angle of reflection are equal:

θi = θr

If several rays of light are parallel and are traveling toward a smooth surface, after reflection, they will be once again propagating in parallel directions, as in Figure 18.2. This is called specular reflection and the reason is that each of the beams will reflect from the same plane surface.

If the surface is not smooth, the outgoing set of rays will no longer be parallel because the roughness of the surface means that different rays have different incident and respective reflection angles. This is called a diffuse reflection, and the way light is reflected at different angles from the rough surface is shown in Figure 18.3.

The rays represented by thicker lines represent the reflected rays and one can see that their direction is dictated by the normal to the surface, which differs between the three cases (the normal is perpendicular on the tangent to the curve at a certain position) .

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