Understanding Refraction and Total Internal Reflection
Diane G. Goldstein Meredith Morgan
Germantown Academy Building Products
Fort Washington, PA Rohm & Haas Company
completion of this activity, the student will:
what an optical fiber is and how it is used in many
understand how the principles of refraction and total
internal reflection explain the transmission of light
energy through an optical fiber.
able to solve problems concerning the design of fiber-optic
why optical fibers are far superior to common copper
transmission lines for carrying information.
experiment works best when the light source is a laser.
Laser light presents some intrinsic dangers, however,
and several simple rules must be obeyed in order to
prevent eye injuries.
look directly into a laser beam source, as even low
power hand held units can cause eye damage due to
the focusing effect of the lens in the eye.
point a laser into someone's eyes, no matter how low
the power of the laser.
deflect a laser beam with a hand held mirror because
you can't control exactly where the beam will go.
use a "beam stop" made out of a cardboard box or similar
surface to "catch" or diffuse the beam, after it exits
your experimental apparatus.
a piece of paper to check for specular reflections
of the laser light. In other words, know where the
beam is at all times!
An addendum includes additional information on cost
and where to purchase starred* items.)
*Laser source: Helium-neon gas laser, either a tabletop
model or a laser pointer clamped to a stand.
container: A long, thin, open top rectangular box works
best, but many other products will work fine and it
would be fun to experiment. We used a container built
from 1/8" acrylic sheet, having internal dimensions
of 12" x 13/8" x 11/2".
& Glo � floor polish added to water, or similar solution
Cardboard box - to "catch" laser beam
tubing -1/16" tubing thickness x 1/2" inner diameter,
cut in 12" lengths Rubber bands
plastic wrap - cut in approximately 2" squares, the
type used for food storage
paper, legal size or 11"x17"
glass and acrylic rods, jars, containers
(note: lab works best in a slightly darkened room.)
Set-up: See Figure 1 below.
How to see a laser beam
beam straight into end of container and observe the
path of the light.
beam at an angle into end of container and observe
the path of the light.
several drops of Mop & Glo � to the water and repeat
steps 1 & 2 above.
Where do you see the light? Can you follow its path
Now you should clearly see the path of the light in
the water. Why?
"cloudy" solution will now allow you to follow the path
of the beam as it travels and further investigate several
properties of light.
of the index of refraction
beam at an angle into the end of the container and
view its path. (For this section, examine only the
portion of the beam before it "bounces" from the inside
of the container. We will analyze the rest of the
path later.) The beam will bend or refract as it enters
a new material medium. This is because the light actually
slows down as it travels from the air to the acrylic
and into the water.
the laser beam OFF: Carefully outline the surface
of the container on the paper and mark with a dot
the point where the beam leaves the laser.
without moving the laser, turn it ON: Put a dot where
the incident beam strikes the entering surface (which
will help you define the path i of the incident beam)
and another dot where the refracted beam, r, first
strikes the second surface. Turn the beam off, remove
the paper and complete the construction similar to
that shown in fig. 2.
You can draw any portion of the beam that is going in
a straight line by marking two dots on the paper and
later joining them with a straight edge to show the
the angles q1 and q2. Both of
these angles are measured from the normal to the incident
of the most important optical measurements for any transparent
material is its refractive index, n. This index is the
ratio of the speed of light in a vacuum to the speed
of light in the material medium.
= cvacuum /cmaterial
practice, the refractive index is measured by comparing
the speed of light in the material to that in air, rather
than a vacuum. This simplifies the measurements and
does not make any practical difference in our lab, since
the speed of light in air is very close to its speed
in a vacuum.
seen in this portion of the lab, the light bends as
it passes through a surface in which the refractive
index changes - for example, passing from the air to
the cloudy water. (The light also bends as it enters
the acrylic material but it bends equally in the other
direction when it exits the material, so the acrylic
layer has no net effect.) The amount of bending depends
on the refractive indices of the two materials, and
the angle of the incident ray striking the boundary
surface. The mathematical relationship between the incident
and transmitted rays is known as Snell's Law: n1sin(q1)
our lab, n1, the index of refraction of air,
is approximately 1, so we can simplify the above expression
= sin (q1) / sin (q2)
if you have not studied trigonometry and are not sure
of the definition of the sine, you can still evaluate
sin (q1) and sin (q2) with your
calculator and determine n, the index of refraction
of the "cloudy" water.
indices of various materials
How does your value of n compare with that of water
in the table? Can you provide a reason(s) for the difference?
Total Internal Reflection
shine the beam straight thought the container. Slowly
change the direction of the beam and watch what happens
to the path of the beam. BE CAREFUL TO MOVE THE CARDBOARD
BOX TO "CATCH" THE REFRACTED AND REFLECTED BEAMS.
MAKE SURE THAT NO BEAM STRAYS INTO SOMEONE ELSE'S
WORK AREA. At certain angles of incidence, notice
how the beam reflects off each side and travels down
the container. When q1 is small, you should
be able to hold a paper on each side of the container
and not see any escaping light. This is due to total
turn the laser to an angle where the beam is no longer
totally reflecting off of the interior sides of the
container, but is partially refracting ("escaping")
out the side. Fine-tune the beam to find the incident
angle largest q1 where none of beam is
refracted (escaping outside.)
to Figure 3 below. The angle indicated by q3
is the critical angle and the angle indicated by q1
is the acceptance angle. Make a sketch of your set-up,
indicating and measuring both the critical and acceptance
angles for the cloudy water solution.
you now have learned that the light will only exhibit
total internal reflection if the incident beam is approaching
the new medium at less than the acceptance angle. When
it does, it will strike the inner surfaces at an angle
greater than the critical angle. This can occur only
when the speed of light inside the medium is less than
its speed outside.
IV: So how
does all this relate to fiber optics?
Fiber optics is simply a method of carrying information
from one point to another using light sent through thin
fibers. An optical fiber is a thin strand of glass or
plastic through which information passes. It serves
the same basic function as copper wire, but the fiber
carries light instead of electricity.
light for communication is not new. Lighthouses have
warned sailors of danger. The English natural philosopher
John Tyndall, in 1870, demonstrated the principle of
guiding light through a series of internal reflections.
The transfer of light energy economically and practically,
however, would not gain promise until research turned
to glass rods as "waveguides" in the 1950's. The term
"fiber optics" was coined in 1956 with the invention
of glass coated rods.
simplest fiber-optic cable consists of two concentric
layers. The inner portion, the core, carries the light.
The outer covering is the cladding. The cladding must
have a lower refractive index than the core. In other
words, light must travel slower in the core than in
the cladding. A cross section of an optical fiber is
shown in figure 4 below. Only light which enters the
fiber at less than some acceptance angle will be totally
What would happen to the path of the light if the materials
of the core and the cladding were suddenly switched?
Think! Between which two boundaries does total internal
reflection occur in this lab? In other words, which
material(s) act as the core and which material(s) act
as the cladding in this lab? (Refer to the wording in
italics in the background material above for hints.
Consider the role of the acrylic box carefully.)
image-transferring bundles of optical fibers had been
developed, it wasn't until after the invention of the
laser that researchers saw the possibilities of combining
fiber-optic technology with laser technology to transmit
communication signals. The laser (Light Amplification
by the Stimulated Emission of Radiation)
emits a narrow beam of coherent light. Coherence - waves
being precisely in phase with one another - is a property
that the laser shares with many types of radio transmitters.
light waves have an important advantage over radio waves:
a much higher frequency. The higher the frequency of
a signal, the more information it can carry.
continued with these two technologies, and eventually
the problem that remained - signal loss (attenuation)
throughout the transmission - was finally solved. High
quality fiber optic "light pipes" were soon
Calculate the frequency of red laser light with a wavelength
of 4.5 x 10-7 m.
Calculate the frequency of radio waves with a wavelength
of 1.0 x 102 m.
many times greater is the information carrying capacity
of red laser light than radio waves?
Calculate the frequency of a sound wave with a wavelength
of 5.9 x 105 m.
many times greater is the information carrying capacity
of red laser light than typical audible sound waves?
V: Loss (attenuation) in your optical "fiber"
slowly turn the laser so that the beam is incident
at various angles. Make a sketch (similar to figure
4) of the complete path of the light for three different
entering angles (q1). Without moving the
container, use a different colored pen or pencil to
mark the points where the beam strikes the side of
the container. Be sure to mark the dot where the laser
originates from the source with the laser OFF.
in the small data table with the required information:
Trial q1 No. of reflections
within the length of the "fiber"
As q1 increases, what happens to the total
number of reflections?
As q1 increases, what happens to the total
distance the light travels along its sawtooth path?
How do you think the signal intensities at the exit
of your simulated fiber compare for these different
light beams? Explain.
VI: Flexible Light Pipes
may have seen some optical fiber cables in school, or
elsewhere. They can be coiled and look like flexible
wire from the outside.
to the following figure for setup.
laser light into one end of a piece of flexible vinyl
tubing and direct the beam leaving the other end onto
a convenient surface.
Is the exiting beam nearly as strong as the entering
What happens as you bend the tube more and more?
Do your observations give evidence that a sufficiently
bent tube no longer exhibits total internal reflection?
be done individually, as homework:
write a two to three paragraph essay describing an application
of fiber optics in our world today. Include some of
the new terminology provided in the lab. Include a diagram
if it will be helpful.
Top Model - from Science Kit, Uniphase Helium Neon
Gas Laser Model 1507-0
Laser Pointer - from Radio Shack, Edmund Scientific,
and the like
from plastic shelves work well.
be built locally at Trident Plastics, Hatboro, PA (1-800-222-2318)at
a cost of approximately $15 each.
can be made very inexpensively by the adventurous by
using 1/8" acrylic sheet (Plexiglas �, Lucite
�, or Acrylite � sheets), solvent cement for
joining acrylic, and a hand held acrylic cutter. All
of these can be purchased from a plastics distributor
Glass Co., Trident Plastics, or some hobby shops.) Build
to dimensions noted in materials list.
from pet (fish) stores, or plastics distributor
such as Trident.
Additional information on fiber optics:
South 48th Street, Ste. 100
company produces an excellent resource booklet and possible
follow up lab to this lab entitled: A Short Course
in Fiber Optics. Call for their Educational
Light Brigade, Inc.
S. 180Th St.
company produces an excellent source of training videos,
and I would recommend the first in this series "Introduction
to Fiber Optic Theory & Fiber
Structure" as a possible addition to this lab.
Optical Fiber Information Center
company sent out an excellent literature package, Fiber
Facts, and a short video. In addition, Corning provided
information on the internet as well.
This experiment is courtesy of