When does total internal reflection happen?

When does total internal reflection happen?

• n_1>n_2
• i>\theta_c (\theta_c is the critical angle)

What can happen?

• The light wave can be refracted
• Or, the light wave can be reflected

Critical angle

The critical angle is the angle at which the light waves stop being refracted, and are instead reflected.

• If the angle of indicence is less than the critical angle, the light ray is refracted.
• If the angle of indicence is more than the critical angle, the light ray is reflected.
• If the angle of incidence is equal to the critical angle,

Calculating the critical angle

\sin\theta_c=\frac{n_2}{n_1}

We can figure this out from snell’s law! The angle of reflection/ refraction will always be 90\degree

• n_1\sin\theta_1=n_2\sin\theta_2
• n_1\sin\theta_c=n_2\sin90
• n_1\sin\theta_c=n_2\times1
• n_1\sin\theta_c=n_2
• sin\theta_c=\frac{n_2}{n_1}

To find just \theta_c (without the \sin):

\theta_c=\sin^{-1}(\frac{n_2}{n_1})