Activity: The Critical Angle and Fiber Optics (Equipment-Based)

In today's activity, you will measure the critical angle and index of refraction for a plastic prism and then use a simulation to investigate the effects of total internal reflection for fiber optics. The readings about these topics are found in the module on Reflection, Refraction, and Fiber Optics.

Equipment needed: Each group needs a laser, a plastic semi-circular prism, a device to vertically spread the laser beam mounted at an appropriate height (such as a cylindrical lens attached to a washer and mounted on a magnetic optical carrier), two pieces of blank paper, and a protractor.

Preparatory Questions:
The following questions should have been answered before the start of the activity. Your instructor may ask you to discuss your answers with group members or as a class before continuing.

Snell's Law states that n₁ sin q₁ = n₂ sin q₂. What does each symbol in the equation represent?
Consider the situation when q₂ = 90^o. q₁ is then called the critical angle q_c. For any angles q₁ > q_c, total internal reflection occurs. Which index of refraction, n₁ or n₂ must be larger for this to occur? Explain.
In the experiment you will perform, the two media will be plastic and air. You will measure the index of refraction for the plastic. Do you expect to see total internal reflection when the light travels into the plastic from the air, when it travels into the air from the plastic, or both? Explain.
What would the critical angle for the plastic be if its index were 1.54?
If you were using total internal reflection to trap light inside a fiber, would the core (inner layer) index have to be less than or greater than the cladding (outer layer) index of refraction? Explain.

Measuring the Critical Angle of a Plastic for a Given Wavelength

LASERS ARE NOT TOYS. DO NOT LOOK INTO THE LASER OR POINT YOUR LASER WHERE IT SHINES IN SOMEONE'S EYES. WHEN YOU ARE NOT USING THE LASER, TURN IT OFF.

Set up the equipment on top of a blank page of paper, as shown to the right. The laser light should shine through a device that spreads the light so you can see the path of the laser on the paper. The light should then strike the curved side of the plastic "prism", travel through the prism, and exit near the middle of the flat side of the prism. Some light will also be reflected off the flat side and exit the curved side.
View from Top (not to scale)
Laser shines through device, then through semicircular prism. Some light is reflected, the rest transmitted. Paper is underneath it all.

1. Rotate the prism, observing the behavior of the light beam exiting the flat face (refracted beam) and the behavior of the beam reflected from the flat face. Start with the flat side perpendicular to (but facing away from) the laser beam, and rotate it counterclockwise, as depicted in the diagram above. Continue rotating it until the flat side is parallel to the laser beam. Describe what happens to the refracted beam and reflected beam as you rotate the prism. How do you know when the critical angle has been reached?

2. Continue rotating the prism and determine whether you can achieve total internal reflection when the light enters the prism, when light leaves the prism, both, or neither? When you observe light entering the prism, the flat side should be facing the laser. (Light striking the curved face does not significantly refract - the angle of incidence is generally close to 0)

3. Rotate the prism back until you have achieved the critical angle for the light traveling from the plastic into air at the flat face. Use a sharp pencil (pen is ok, but sharp pencil is best) to CAREFULLY mark the following points:

The point at which light enters the front face of the prism (point A)

The point at which the light hits the back face of the prism (point B)

Another point along the back face of the prism (point C)

The point at which light exits the curved face of the prism (point D).

Remove the plastic, label the points, and CAREFULLY draw the following lines, using a ruler and making sure the lines are longer than your protractor:

A line connecting points A and B, representing the incident ray

A line connecting points B and C, representing the back face of the prism (and the refracted ray)

A line connecting points B and D, representing the reflected ray

This sheet represents raw data, so make sure the names of all group members are on it.

4. Measure the angle between the incident ray and the reflected ray, estimating angles down to the nearest tenth of a degree. Be sure to line up your protractor as CAREFULLY as you can. A small error in measurement can lead to bad results in today's experiment!

5. Calculate the critical angle from your angle in the previous question. How are they related?

6. How does this critical angle compare to the one you predicted for plastic in the Preparatory Questions?

7. Use your measured value of the critical angle to determine the index of refraction of your prism. Discuss your result in light of any discrepancies found in the previous question.

Applications to Optical Fibers

Go to this simulation of optical fibers by the Universitat Oldenburg, and answer the following questions. A few notes about the simulation:

The simulation is located at the bottom of the web page.
After you change parameters, you must click on the Trace button to see the effect of the new settings.
The angle denoted by i in this simulation (the angle of entry) is denoted by q₀ in the on-line readings for this course.
Assume that the fiber is in air, so n₀ is 1.0 throughout this activity.
Predict the answers to questions 8-9 before checking with the simulation.

8.	Will the angle of incidence i affect whether or not the light is totally internally reflected as it enters the fiber? If so, how? If not, why not?
9.	Based on what you know about total internal reflection, what range of values of n₂ will keep the light trapped in the fiber? (You may assume the angle of incidence on the edge of the fiber is larger than the critical angle) Try out ns from your range and check.
10.	Some of the n₂ values you expected to trap light in the fiber might have let light escape in the simulation due to the angle at which light strikes the edge of the fiber. In these situations would you need to increase or decrease the angle at which light strikes the top edge of the fiber (as measured to the normal) to trap the light?
11.	Does this desired increase or decrease in the angle at the edge of the fiber correspond to an increase or decrease of the incident angle i at which the light enters the fiber? Use the simulation to verify your answer.
12.	Set the indices to n₁=1.54 and n₂ = 1.50, and find the largest value of i that results in total internal reflection by trying different values of i. Compare your result to the cut-off angle given by the simulation.
13.	If you were designing a fiber, do you think you would prefer for your light to enter at an angle close to (but still less than) the cut-off angle, or at a much smaller angle close to zero degrees? What potential benefits do you envision this having?

1.	Rotate the prism, observing the behavior of the light beam exiting the flat face (refracted beam) and the behavior of the beam reflected from the flat face. Start with the flat side perpendicular to (but facing away from) the laser beam, and rotate it counterclockwise, as depicted in the diagram above. Continue rotating it until the flat side is parallel to the laser beam. Describe what happens to the refracted beam and reflected beam as you rotate the prism. How do you know when the critical angle has been reached?
2.	Continue rotating the prism and determine whether you can achieve total internal reflection when the light enters the prism, when light leaves the prism, both, or neither? When you observe light entering the prism, the flat side should be facing the laser. (Light striking the curved face does not significantly refract - the angle of incidence is generally close to 0)
3.	Rotate the prism back until you have achieved the critical angle for the light traveling from the plastic into air at the flat face. Use a sharp pencil (pen is ok, but sharp pencil is best) to CAREFULLY mark the following points: The point at which light enters the front face of the prism (point A) The point at which the light hits the back face of the prism (point B) Another point along the back face of the prism (point C) The point at which light exits the curved face of the prism (point D). Remove the plastic, label the points, and CAREFULLY draw the following lines, using a ruler and making sure the lines are longer than your protractor: A line connecting points A and B, representing the incident ray A line connecting points B and C, representing the back face of the prism (and the refracted ray) A line connecting points B and D, representing the reflected ray This sheet represents raw data, so make sure the names of all group members are on it.
4.	Measure the angle between the incident ray and the reflected ray, estimating angles down to the nearest tenth of a degree. Be sure to line up your protractor as CAREFULLY as you can. A small error in measurement can lead to bad results in today's experiment!
5.	Calculate the critical angle from your angle in the previous question. How are they related?
6.	How does this critical angle compare to the one you predicted for plastic in the Preparatory Questions?
7.	Use your measured value of the critical angle to determine the index of refraction of your prism. Discuss your result in light of any discrepancies found in the previous question.