Lesson 3: 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, the primary focus was the reflective behavior
of light waves at the boundary. In this unit, our primary
interest in this unit 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 be 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
reflection 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 equation
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 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.
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