Total internal reﬂection takes place when light is reﬂected back into the medium because the angle of incidence is greater than the critical angle.
Each medium has its own unique critical angle. For example, the critical angle for glass is 42◦,
and that of water is 48.8◦. We can calculate the critical angle for any medium.
Calculating the Critical Angle
Now we shall learn how to derive the value of the critical angle for two given media. The process is fairly simple and involves just the use of Snell’s Law that we have already studied.
To recap, Snell’s Law states:
n1 sin θ1 = n2 sin θ2
where n1 is the refractive index of material 1, n2 is the refractive index of material 2, θ1 is the angle of incidence and θ2 is the angle of refraction.
For total internal reﬂection we know that the angle of incidence is the critical angle.
θ1 = θc.
However, we also know that the angle of refraction at the critical angle is 90◦. So we have:
θ2 = 90◦
We can then write Snell’s Law as:
Take care that for total internal reﬂection the incident ray is always in the denser medium.
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