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Overview

Optical fibers transmit light signals and are widely used in the telecommunications industry to transmit data over long distances. Light travels through the core material of an optical fiber by essentially repeatedly bouncing off the cladding material that surrounds the core. Understanding refraction and how light behaves at the boundary of two different materials is the basis for understanding how fiber optic lines work. In particular, total internal reflection occurs when light travels in a material with a higher index of refraction toward a material with a lower index of refraction and the angle of incidence is greater than the critical angle.

In this lesson, students investigate through experimentation, discussion, and video the phenomenon of total internal reflection and its relationship to fiber optics. Students also watch a video about dispersion and discuss the implications for fiber optics.

Note: This is the second of two optics lesson plans. You may want to precede this lesson with The Index of Refraction Lesson Plan.

Objectives

• Explain the critical angle, total internal reflection, and how the principles apply to optical fiber
• Explain how dispersion causes rainbows and limits data rate in a fiber optic system

Grade Level: 9–12

Suggested Time

• 1–2 class periods

Media Resources

• Laser Waterfall Video
• Light and Color Video

Materials

Computers with Internet connection

For each group:

• Science notebooks
• Laser pointer
• Plastic refraction kits. If plastic kits are not available, use slabs of very stiff gelatin made from unflavored gelatin powder. For this, you will need:
  • Unflavored gelatin powder
  • Boiling water
  • Bowl and spoon
  • Cooking oil spray
  • Flat-bottom pan
  • Plastic knife to cut gelatin

Before the Lesson

• If possible, arrange computer access for all students to work individually or in pairs.
• Gather all materials.
• If plastic refraction sets are not available, students can measure the index of refraction of gelatin. Unflavored gelatin powder can be purchased in grocery stores. Prepare the powder with half of the boiling water specified on the package and stir very well until all of the gelatin is dissolved. Spray a flat-bottom pan with oil and pour in the mixture. The gelatin should be at least 1.5 cm thick. Let the gelatin stand until firm; refrigerate until ready to use if the room is warm. Each group will need a rectangle about 6 cm by 8 cm.

The Lesson

Part I: The Critical Angle, Total Internal Reflection, and Optical Fiber

1. Review with students what happens when light travels from a material with a higher index of refraction to a material with a lower index of refraction. In this case, the refracted angle is larger than the incident angle. Illustrate this situation with a drawing: show a small incident angle and a larger refracted angle. Ask students:

1. What happens if the incident angle is made slightly larger?
2. Is there a limit to how large the incident angle can be?
3. What happens when light is incident at an angle larger than this limiting angle?

2. Have students explore the critical angle by cutting the gelatin slab to form a right triangle (or use a triangular plastic refraction shape). Direct the laser through one of the sides and watch the behavior of the beam as the angle of incidence changes at the hypotenuse edge. With plastic it should be easy to observe the change from refraction to total internal reflection at the critical angle. Unless the gelatin edge is very clean, the change to total internal reflection will not be as abrupt as it is with plastic.

3. Show students the Laser Waterfall Video. Ask students to explain how the concept of total internal reflection applies to optical fibers.

4. Have students investigate total internal reflection by cutting a thin strip from one of the gelatin slabs (about 2 cm wide and as long as possible). Ask students to direct the laser pointer so that the beam undergoes total internal reflection. Discuss with students:

1. Does any light leak out the side?
2. Does it matter if the gelatin piece is bent?
3. Is there a limit to how much the "fiber" can bend before light leaks out the side?
4. What does this mean for light loss in a real optical fiber as it bends around obstacles?

Part II: Dispersion

5. Dispersion is the dependence of index of refraction upon wavelength. That is, the index of refraction is not the same for all colors of the spectrum. Show students the Light and Color Video. Discuss the following:

1. How does dispersion explain the formation of rainbows?
2. What effect might dispersion have on a pulse of white light traveling down an optical fiber?
3. Would the length of the fiber have an effect on the pulse of light?
4. How does dispersion limit data rates in fiber optics?

6. Even though fiber optic systems use LEDs or lasers instead of white light, there is still a (small) range of wavelengths present in the light. If some wavelengths travel faster they will reach the end of the fiber before the slower wavelengths. Draw a square input pulse and discuss with students what the pulse will look like if different wavelengths reach the end of the fiber at different times. A useful analogy is to think about the density of runners at the start of a marathon and at the finish line; a hundred runners may start at the same time as part of the same "pulse," but since each runner travels at a different rate, they will spread out over the course of the race and have different finishing times.

Check for Understanding

1. Have students summarize the general rules for refraction:
   1. How does light bend going from high n to low n?
   2. In which direction is there a critical angle?
   3. What happens at the critical angle?
   4. What happens if the incident angle is larger than the critical angle?
2. Have students discuss the following:
   1. In binoculars, prisms are often used to reflect and direct the light so that you see a correctly oriented image when you look through the eyepieces. How can a prism be used to reflect light? Why do you think a prism would be preferable to a mirror for use in binoculars?
   2. An optical fiber uses total internal reflection to transmit light over long distances. What are some applications of fiber optics? What are some limitations of optical fibers?