Instructor's Guide to Preparation for The Critical Angle and Fiber Optics Activity

In this activity, you will 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.

1. Snell's Law states that n₁ sin q₁ = n₂ sin q₂.  What does each symbol in the equation represent?
n_i represents the index of refraction of medium i; q_i represents the angle between the path of light and the normal to the surface in medium i.
 
2. 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.
For total internal reflection (TIR) to occur, light must bend away from the normal.  Another way to say this is that q₂ > q₁ .  Sin q₂ will then be greater than sin q₁, since sine increases with angle for angles less than 90^o.  If the angle in medium 2 is larger, Snell's Law can only be satisfied if medium 2 has a smaller index of refraction.  Thus n₂ < n₁ if TIR occurs as light moves from medium 1 to medium 2.  Total internal reflection can only occur when light moves from a denser medium (higher n) to a rarer medium (lower n).
 
3. 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.
In the experiment, air has the smaller index of refraction, so TIR will occur as the light travels from the plastic into the air.
 
4. What would the critical angle for the plastic be if its index were 1.54?
n₁ sin q₁ = n₂ sin q₂.
n₁ sin q_c = n₂ sin 90^o = n₂, so
q_c = sin^-1(n₂/n₁) = sin^-1(1.00/1.54) = 40.5^o.
 
5. 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.
Since TIR occurs when light moves into a rarer medium, the index of the core would have to be greater than the index of the cladding.

If it is in keeping with class policy, discuss your answers with classmates, either before coming to class or at the start of class.  Does everyone have the same answers, or are there differing opinions?