Total Internal Reflection
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 behaviorsinclude 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 that 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 that points in the direction that 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 intotwo other rays
at the point of incidence with the boundary. The reflected waves are the waves
that bounce off the boundary and head back upwards and the reflected ray is the ray
that points in the direction that the reflected waves are traveling. The
reflected ray is drawn in green on the diagram at the right. The refracted
waves are the waves that are transmitted across the boundary and continue
moving downwards, only at a different angle than before. The refracted ray is
the ray that points in the direction that 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 that 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 that 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 (Θi) and the angle
of refraction (Θr) is given by the
following equation
ni • sine(Θi)
= nr • sine(Θr)
where 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 occurs 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.
Laser light shown passing into a
hemi-cylindrical dish filled with water. The light enters the water (at the
curved side of the dish) along the normal line; no bending occurs upon entry.
The light continues through the water along a straight line until it reaches
the boundary with air (at the flat side of the dish). The angle of incidence in
the water is just short of 48°. Since the angle of incidence is just less than
the air-water critical angle of about 48.6°, there is still a little refraction
in addition to the reflection. The refracted ray can be seen at about 80°.