Total Internal Reflection
Boundary Behavior Revisited
Earlier in this unit, the boundary behavior of light waves was discussed. It was mentioned that a light wave doesn't just stop when it reaches the end of the medium. Rather, the light wave undergoes certain behaviors when it encounters the end of the medium - such behaviors include reflection, transmission/refraction, and diffraction. In Unit 13 of The Physics Classroom Tutorial, the primary focus was the reflective behavior of light waves at the boundary. In this unit, our primary interest has been the refractive behavior of light waves at the boundary. In Lesson 3, we will investigate the connection between light reflection and light refraction.
A light wave, like any wave, is an energy-transport phenomenon. A light wave transports energy from one location to another. When a light wave strikes a boundary between two distinct media, a portion of the energy will be transmitted into the new medium and a portion of the energy will be reflected off the boundary and stay within the original medium. The actual percentage of energy which is transmitted and reflected is dependent upon a number of variables; these will be discussed as we proceed through Lesson 3. For now, our concern is to review and internalize the basic concepts and terminology associated with boundary behavior. Reflection of a light wave involves the bouncing of a light wave off the boundary, while refraction of a light wave involves the bending of the path of a light wave upon crossing a boundary and entering a new medium. Both reflection and refraction involve a change in direction of a wave, but only refraction involves a change in medium.
The diagram at the right
shows several wavefronts approaching a boundary between two
media. These wavefronts are referred to as the incident
waves and the ray which points in the direction 
which
they are traveling is referred to as the
incident ray. The
incident ray is drawn in blue on the diagram at the right.
Notice on the diagram that the incident ray leads
into two other rays at the point of incidence with the
boundary. The reflected waves are the waves which bounce off
the boundary and head back upwards and the
reflected ray is the ray
which points in the direction which the reflected waves are
traveling. The reflected ray is drawn in green on the
diagram at the right. The refracted waves are the waves
which are transmitted across the boundary and continues
moving downwards, only at a different angle than before. The
refracted ray is the ray which points in the direction which
the refracted waves are traveling. The refracted ray is
drawn in red on the diagram at the right. At the
point of incidence (the
point where the incident ray strikes the boundary), a
normal line is drawn.
The normal line is always drawn perpendicular to the surface
at the point of incidence. The normal line creates a variety
of angles with the light rays; these angles are important
and are given special names. The angle between the incident
ray and the normal is the angle of
incidence. The angle between the reflected ray
and the normal is the angle of
reflection. And the angle between the refracted
ray and the normal is the angle of
refraction.
The fundamental law which governs the reflection of light is called the law of reflection. Whether the light is reflecting off a rough surface or a smooth surface, a curved surface or a planar surface, the light ray follows the law of reflection. The law of reflection states that
When a light ray reflects off a surface, the angle of incidence is equal to the angle of reflection.
The fundamental law which governs the refraction of light is Snell's Law. Snell's Law states that
When a light ray is transmitted into a new medium, the relationship between the angle of incidence and the angle of refraction is given by the following equationwhere the ni and nr values represent the indices of refraction of the incident and the refractive medium respectively.
As we proceed through this Lesson, we will see that there is a connection between the reflection and the refraction of light. Each of these two behaviors usually occur together. But as we will see, there are two conditions, which when both met, will cause the light waves to undergo reflection without any accompanying refraction.