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

In today's activity, you will use simulations to measure the critical angle for a plastic prism and then 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.

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

Go to the web site http://www.physics.northwestern.edu/ugrad/vpl/optics/snell.html. You will see a simulation of light moving from one medium at the top of the screen to another medium below. n₁ and n₂ represent the indices of refraction in the top and bottom medium, respectively. Notice that the different color lines do NOT represent different colors of light. The light is monochromatic laser light. The different colors identify the incident ray (blue), the reflected ray (green) and the refracted ray (red). View of Simulation
Blue incident ray and Green reflected ray in material of n_1. Red transmitted ray in material of n_2.

1. The default settings have n₁ less than n₂. Try entering different angles of incidence q₁, ranging from 1^o to 89^o. Describe what happens to the refracted beam and reflected beam as you increase the angle of incidence. Do you ever achieve total internal reflection? How do you know?

2. Now set n₁=1.54 and n₂=1.00 to simulate light exiting plastic and entering air. Again, enter different angles of incidence q₁ ranging from 1^o to 89^o. Do you ever achieve total internal reflection with this set up? How do you know? Is this what you predicted in the Preparatory Questions?

3. You will next determine the value of the critical angle for this interface by trying various values of q₁, and recording the resulting q₂, (or indicating whether total internal reflection has occurred). If you have not achieved total internal reflection for a given value of q₁, should you increase or decrease q₁in your next attempt?

4. If you have achieved total internal reflection for a given value of q₁, does that necessarily mean that q₁ is the critical angle? How will you know when the critical angle has been reached?

5. Write down at least 10 values of q₁ which you tried as you looked for the critical angle, along with the resulting sin q₂ given by the simulation. Use the given sin q₂ to calculate q₂. Your values of q₁ should show a gradual approach to the critical angle.

6. Record your value for the critical angle to the nearest 0.1 degree as found from the simulation. How does this critical angle compare to the one you predicted for plastic in the Preparatory Questions?

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.

7.	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?
8.	Assume the core is composed of the plastic you used in the previous part of the activity, with n₁ = 1.54. Change n₁ to this value and Trace the ray, keeping the other variables at their default settings. Is the light trapped in the fiber? 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.	The default settings have n₁ less than n₂. Try entering different angles of incidence q₁, ranging from 1^o to 89^o. Describe what happens to the refracted beam and reflected beam as you increase the angle of incidence. Do you ever achieve total internal reflection? How do you know?
2.	Now set n₁=1.54 and n₂=1.00 to simulate light exiting plastic and entering air. Again, enter different angles of incidence q₁ ranging from 1^o to 89^o. Do you ever achieve total internal reflection with this set up? How do you know? Is this what you predicted in the Preparatory Questions?
3.	You will next determine the value of the critical angle for this interface by trying various values of q₁, and recording the resulting q₂, (or indicating whether total internal reflection has occurred). If you have not achieved total internal reflection for a given value of q₁, should you increase or decrease q₁in your next attempt?
4.	If you have achieved total internal reflection for a given value of q₁, does that necessarily mean that q₁ is the critical angle? How will you know when the critical angle has been reached?
5.	Write down at least 10 values of q₁ which you tried as you looked for the critical angle, along with the resulting sin q₂ given by the simulation. Use the given sin q₂ to calculate q₂. Your values of q₁ should show a gradual approach to the critical angle.
6.	Record your value for the critical angle to the nearest 0.1 degree as found from the simulation. How does this critical angle compare to the one you predicted for plastic in the Preparatory Questions?