Core Unit III: Light
C. Refraction

2). Total Internal Reflection

Key Concepts

An incident ray striking a boundary from a more refractive medium to a less refractive medium at an angle greater than the critical angle experiences total internal reflection.

Total internal reflection is only possible if light is travelling from a more refractive medium to a less refractive medium.
(i.e., n₂ < n₁)

As the angle of incidence increases, the angle of refraction approaches 90^o.

The critical angle is the angle of incidence for which the angle of refraction is 90^o. At this angle the refracted ray glances parallel to the boundary.

The incident ray undergoes total internal reflection at any angle greater than the critical angle.

If the incident angle is less than or equal to the critical angle, the refracted ray will be bent away from the normal (provided that n₂ < n₁).

A high relative index of refraction (the ratio n₂/n₁) will result in a smaller critical angle.

The critical angle (i_c) can be determined from the general form of Snell's Law. At the critical angle, <R = 90^o, so sinR = 1, and

sin 90 ^o = 1

so,

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: total internal reflection, critical angle.

2. Solve problems involving the refraction of light.

3. Recognize situations in which total internal reflection could occur.

4. Determine the critical angle for light travelling from any medium into some other medium.

5. Recognize that the critical angle depends on the relative index of refraction between two media.

6. Explain how an incident ray, travelling towards a medium with a lower index of refraction, would behave if the angle of incidence were smaller than the critical angle, the same size as the critical angle, or larger than the critical angle.

Teaching Suggestions, Activities and Demonstrations

1. Demonstrate total internal reflection. Some students may not be aware that they have likely seen it occurring before.

2. Working individually or in groups, students can research the use of fibre optics in communication systems.