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    Fiber Optics: Refraction & Total Internal Reflection
    A High School Physics Lab
    For Science Labs, Lesson Plans, Class Activities & Science Fair Projects







    This experiment is courtesy of 

    Understanding Refraction and Total Internal Reflection

    Developers:

    Diane G. Goldstein Meredith Morgan

    Germantown Academy Building Products Research

    Fort Washington, PA Rohm & Haas Company

     

    Grade Level:

    9 through 12

     

    Discipline:

    Physics

     

    Goals:

    Upon completion of this activity, the student will:

    1. know what an optical fiber is and how it is used in many different applications.
    2. understand how the principles of refraction and total internal reflection explain the transmission of light energy through an optical fiber.
    3. be able to solve problems concerning the design of fiber-optic cables.
    4. understand why optical fibers are far superior to common copper transmission lines for carrying information.

    Safety Notes:

    This 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.

    1. Never 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.
    2. Never point a laser into someone's eyes, no matter how low the power of the laser.
    3. Never deflect a laser beam with a hand held mirror because you can't control exactly where the beam will go.
    4. Always 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.
    5. Use a piece of paper to check for specular reflections of the laser light. In other words, know where the beam is at all times!

    Materials:

    (Note: 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.

    *Acrylic 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".

    Mop & Glo � floor polish added to water, or similar solution

    Cardboard box - to "catch" laser beam

    *Vinyl tubing -1/16" tubing thickness x 1/2" inner diameter, cut in 12" lengths Rubber bands

    Clear plastic wrap - cut in approximately 2" squares, the type used for food storage

    Protractor

    Ruler

    White paper, legal size or 11"x17"

    Various glass and acrylic rods, jars, containers

     

    Procedure:

    (note: lab works best in a slightly darkened room.)

    Materials Set-up: See Figure 1 below.

     

    Part I: How to see a laser beam

    1. Shine beam straight into end of container and observe the path of the light.
    2. Shine beam at an angle into end of container and observe the path of the light.
    3. Add several drops of Mop & Glo � to the water and repeat steps 1 & 2 above.

    Q1: Where do you see the light? Can you follow its path completely?

    Q2: Now you should clearly see the path of the light in the water. Why?

    The "cloudy" solution will now allow you to follow the path of the beam as it travels and further investigate several properties of light.

     

    Part II: Investigation of the index of refraction

    1. Shine 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.
    2. With 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.
    3. Now, 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.

    NOTE: 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 light path.

    Measure the angles q1 and q2. Both of these angles are measured from the normal to the incident surface.

    One 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.

    n = cvacuum /cmaterial

    In 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.

    As 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) = n2sin(q2)

    In our lab, n1, the index of refraction of air, is approximately 1, so we can simplify the above expression to:

    n = sin (q1) / sin (q2)

    Even 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.

     

    Table 1: Refractive indices of various materials

    Material n

    vacuum1.0

    air 1.00029

    water 1.33

    acrylic 1.45-1.6

    glass 1.46-1.6

    Q3: How does your value of n compare with that of water in the table? Can you provide a reason(s) for the difference?

     

    Part III: Total Internal Reflection

    1. Again, 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 internal reflection.
    2. Finally, 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.)
    3. Refer 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.

    So 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.

     

    Part IV: So how does all this relate to fiber optics?

    Background: 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.

    Using 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.

    The 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 internally reflected.

    Q4: What would happen to the path of the light if the materials of the core and the cladding were suddenly switched?

    Q5: 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.)

    Although 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.

    But 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.

    Research 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 commercially available.

    Q6: 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.

    How many times greater is the information carrying capacity of red laser light than radio waves?

    Q7: Calculate the frequency of a sound wave with a wavelength of 5.9 x 105 m.

    How many times greater is the information carrying capacity of red laser light than typical audible sound waves?

     

    Part V: Loss (attenuation) in your optical "fiber"

    1. Again, 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.
    2. Fill in the small data table with the required information:

    Trial q1 No. of reflections within the length of the "fiber"

    1

    2

    3

     

    Q8: As q1 increases, what happens to the total number of reflections?

    Q9: As q1 increases, what happens to the total distance the light travels along its sawtooth path?

    Q10: How do you think the signal intensities at the exit of your simulated fiber compare for these different light beams? Explain.

     

    Part VI: Flexible Light Pipes

    You may have seen some optical fiber cables in school, or elsewhere. They can be coiled and look like flexible wire from the outside.

    Refer to the following figure for setup.

    Shine laser light into one end of a piece of flexible vinyl tubing and direct the beam leaving the other end onto a convenient surface.

    Q11: Is the exiting beam nearly as strong as the entering beam?

    Q12: What happens as you bend the tube more and more?

    Q13: Do your observations give evidence that a sufficiently bent tube no longer exhibits total internal reflection?

    **********************************************************************

    To be done individually, as homework:

    Please 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.

    **********************************************************************

     

    Addendum:

    1. Material Suppliers:

    Laser source:

    Table Top Model - from Science Kit, Uniphase Helium Neon Gas Laser Model 1507-0
    Laser Pointer - from Radio Shack, Edmund Scientific, and the like

    Acrylic container:

    Drawers from plastic shelves work well.

    Containers can be built locally at Trident Plastics, Hatboro, PA (1-800-222-2318)at a cost of approximately $15 each.

    Containers 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 (Doylestown Glass Co., Trident Plastics, or some hobby shops.) Build to dimensions noted in materials list.

     

    Vinyl tubing:

    Available from pet (fish) stores, or plastics distributor such as Trident.

     

    2. Additional information on fiber optics:

    Industrial Fiber Optics
    627 South 48th Street, Ste. 100
    Tempe, AZ 85271
    (601) 804-1227

    This 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 Products Catalog.

    The Light Brigade, Inc.
    7639 S. 180Th St.
    Kent, Washington 98032
    (206) 251-1240

    This 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.

    Corning Optical Fiber Information Center

    (800) 525-2524

    This 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 



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    Last updated: June 2013
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