1. Review of Snell’s Law & Refraction Calculations
A ray of light passes from water into sapphire at an angle of 37°. What is the angle of refraction?

2. Total Internal Reflection

3. Recall... How does Light Bend?
When light travels from a slower medium into a faster medium, it bends away from the normal at the boundary of the two media. For example, when light travels from acrylic into air.

4. Total Internal Reflection: occurs when incident ray of light is NOT refracted, but instead, it is entirely reflected back into the first medium.

5. The angle of refraction continues to increase as the angle of incidence increases. Eventually the angle of refraction will become 90°.
At a certain angle of incidence, called the critical angle, the refracted ray follows a path exactly 90° from the normal.
The diagram shows the refracted ray following a path exactly along the surface of the water (boundary line) (θR = 90°).
Light is “trapped” at the interface between the air and water. The refracted ray does not exit the medium! θR
Critical Angle: Angle of incidence that produces an angle of refraction of 90°
This angle is dependent on the n value of the medium in question.

6. If the angle of incidence is increased even farther (past the critical angle that made the refracted angle 90o), then the light ray is no longer refracted at all. Instead, it is completely reflected back into the medium.
Therefore, total internal reflection takes place when both conditions below are met:
Light travels from a slower (more dense) medium to a faster (less dense) medium
Angle of incidence is greater than the critical angle

7. In Summary...
Angle of incidence less than the critical angle. Refraction occurs.
Angle of incidence equal to critical angle. Light is refracted along the boundary line between the two mediums.
Angle of incidence greater than the critical angle. Total Internal Reflection occurs.

8. Applications of Total Internal Reflection
The cut of the diamond faces along the high index of refraction for diamonds (n = 2.42) results in the total internal reflection of light.
Diamonds have a very small critical angle (24.4°) so a lot of incident light undergoes total internal reflection inside the diamond.
Light rays can bounce around several times inside the diamond before eventually exiting through the top face = creates a “sparkling” effect.

9. Applications of Total Internal Reflection
Occurs in fibre optic cables to allow light, telephone and internet communications to be transmitted over great distances and around corners without ever leaving the cable.
Also found in endoscopes that surgeons use to see internal organs during surgery.
Cables are made of glass or lucite (plastic) and are used to transmit light.
The cable has a small critical angle so that the light entering it will have an angle of incidence greater than the critical angle, and will undergo TIR. The light bounces back and forth and is transmitted very quickly.