Peoples Physics Concepts

16.5 Total Internal Reflection

16.5 Total Internal Reflection

• Describe total internal reflection and the critical angle.


• Derive the critical angle and solve for it in real life applications.

Students will learn about total internal reflection. More specifically, they will learn what the critical angle is, how it

is derived and how to solve for it in real life applications.

Key Equations

θC=sin−^1 nn^21 ; whereθCis the critical angle, n 1 is the index of refraction of the material where the light emanates

from and n 2 is the index of the material outside.

Guidance

Total internal reflectionoccurs when light goes from a slow (high index of refraction) medium to a fast (low index

of refraction) medium. With total internal reflection, light refracts so much it actually refracts back into the first

medium. This is how fiber optic cables work: no light leaves the wire.

Example 1

You have some unknown material and you would like to determine it’s index of refraction. You find that you are

able to create total internal reflection when the material submerged in water, but not when submerged in cooking

oil. (a) Can you give a range for the index of refraction? (b) you are able to determine the critical angle in water to

be 71.8 degrees; what is the index of refraction of this material?

Solution

(a): Since it is not possible to create total internal refraction when going from a material with a higher index of

refraction to a lower index of refraction, we know that the index of refraction of this material must be between 1.33

(water) and 1.53 (cooking oil).

(b): We can use the equation given above to determine the index of refraction of the unknown material.

θc=sin−^1 (

n 2

n 1

)

n 1 =

n 2

sin(θc)

n 1 =

1. 33

sin( 71. 8 )

n 1 = 1. 40