Refraction and the Ray Model of
Light
Refraction at a Boundary
Boundary Behavior
A
wave doesn't just stop when it reaches the end of the medium.
Rather, a wave will undergo certain behaviors when
it encounters the end of the medium. Specifically, there will be some
reflection off the boundary and some transmission into the new medium. The
transmitted wave undergoes refraction (or bending) if it approaches the
boundary at an angle. If the boundary is merely an obstacle implanted within
the medium, and if the dimensions of the obstacle are smaller than the
wavelength of the wave, then there will be very noticeable diffraction of the
wave around the object. The reflection, refraction, and diffraction of waves
were first introduced in Unit 10 of
The Physics Classroom tutorial. In Unit 11 of
The Physics Classroom Tutorial, the reflection, refraction, and diffraction
of sound waves was discussed. Since light is a wave, it too will undergo these
same behaviors when it reaches a boundary
between two media. The boundary behavior of
light waves has already been introduced in Unit 12 of
The Physics Classroom Tutorial. In this unit, we will focus on the refraction
of light in great detail. We will explore the conceptual and mathematical
principles governing the bending of waves as they cross the boundary between
two media. To understand light refraction, we will need to back up a few steps
and investigate the behavior of waves when
they reach the end of a medium.
Boundary Behavior for Waves on a Rope
Suppose
that there is a thin rope attached to a thick rope, with each rope held at
opposite ends by people. And suppose that a pulse is introduced by the person
holding the end of the thin rope. If this is the case, there will be an incident
pulse traveling in the less dense medium (thin rope) towards the boundary with
a more dense medium (thick rope).
Upon reaching the boundary, two behaviors will
occur.
· A portion of the energy
carried by the incident pulse is reflected and returns towards the left end of
the thin rope. The disturbance that returns to the left after bouncing off the
boundary is known as the reflected pulse.
· A portion of the energy
carried by the incident pulse is transmitted into the thick rope. The
disturbance that continues moving to the right is known as the transmitted pulse.
These two behaviors -
reflection and transmission - were first introduced in Unit 10 of The Physics Classroom. In that
unit, it was mentioned that the passage of the energy from the incident medium
into the transmitted medium was accompanied by a change in speed and
wavelength. In the case of a pulse crossing the boundary from a less dense
medium into a more dense medium, the speed
and the wavelength are both decreased. On the other hand, if a pulse crosses
the boundary from a more dense medium into a
less dense medium, the speed and the wavelength are both increased.
Refraction of Light Waves
The
above discussion was limited to the behavior of a
wave on a rope. But what if the wave is a light wave traveling in a
three-dimensional medium? For example, what would happen if a light wave is
traveling through air and reaches the boundary with a glass surface? How can
the reflection and transmission behavior of a
light wave be described? First, the light wave behaves like the wave on the
rope: a portion of the wave is transmitted into
the new medium (glass) and a portion of the wave reflects off the air-glass
boundary. Second, the same wave property changes that were observed for the
wave on the rope are also observed for the light wave passing from air into
glass; there is a change in speed and wavelength of the wave as it crosses the
air-glass boundary. When passing from air into glass, both the speed and the
wavelength decrease. Finally, and most importantly, the light is observed to
change directions as it crosses the boundary separating the air and the glass.
This bending of the path of light is known as refraction. A
one-word synonym for refraction is bending.
The transmitted wave experiences this refraction at the boundary. As seen in
the diagram at the right, each individual wavefront is
bent only along the boundary. Once the wavefront has
passed across the boundary, it travels in a straight line. For this reason,
refraction is called a boundary behavior. A ray is
drawn perpendicular to the wavefronts; this ray
represents the direction that the light wave is traveling. Observe that the ray
is a straight line inside of each of the two media, but bends at the boundary.
Again, refraction is a boundary behavior.
The
Ray Model of Light
In
this unit, we will rely heavily on the use of rays to represent the direction
in which light is moving. While we often think of light behaving as a wave, we will
still find it useful to represent its movement through a medium using a line
segment with an arrowhead (i.e., a ray) to depict the refraction of light. The
ray is constructed in a direction perpendicular to the wavefronts of the light wave; this
accurately depicts the light wave's direction. In this sense, we are viewing
light as behaving as a stream of particles that head in the direction of the
ray. The idea that the path of light can be represented by a ray is known as
the ray model of light. The same ray model was utilized in Unit 13 of The Physics Classroom
Tutorial to discuss
the reflection of light waves.
