The Critical Angle

The Critical Angle

The previous page qualitatively examined the topic of total internal reflection. Here we will see how the phenomenon falls out naturally as a consequence of Snell's Law.
$Light bends away when traveling into a rarer medium, so the angle of refraction is greater than the angle of incidence.$
Consider the water-air interface described on the previous page and reproduced here to the right. Snell's Law for this interface is

n₁ sin θ₁ = n₂ sin θ₂.

The critical angle is reached when θ₂ is 90 degrees:

n₁ sin θ_c = n₂ sin 90^o = n₂

Thus we have the following expression for the critical angle:

sin θ_c = n₂/n₁.

Note that this use of mathematics agrees with our qualitative assessment from the previous page:

The critical angle is only defined if light travels from a denser medium to a rarer medium. If light were traveling the other way, n₂ > n₁, and sin θ_c would therefore be greater than 1.
Any angle θ₁ greater than the critical angle results in no light crossing the interface. If θ₁ > θ_c, then sin θ>₁ > n₂/n₁, and Snell's Law would then require that sin θ₂ be greater than 1.

Sample Problems

Practice Exercises

At-Home Assignments

What does all this have to do with information transfer?
Continue to the next section to find out!