Friday, January 15, 2010

Total Internal Reflection

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:

n1 sin θ1 = n2 sin 90◦

Take care that for total internal reflection the incident ray is always in the denser medium.

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