C.3.4—Total internal reflection

Check the two conditions

Total internal reflection can occur only when a wave travels from a higher-index medium to a lower-index medium, and the incidence angle is greater than the critical angle. At the critical angle, the refracted ray travels along the boundary: $\theta_2=90^\circ$.

Calculate the critical angle

From Snell’s law, $\sin\theta_c=n_2/n_1$ for $n_1>n_2$. For a dense medium to air, $n_2\approx1$, so $\sin\theta_c=1/n_1$.

Use the boundary picture

For incidence below $\theta_c$, there is a refracted ray. At $\theta_c$, it grazes the boundary. Above $\theta_c$, no refracted ray propagates into the lower-index medium and all the light is reflected back into the denser medium.

Common trap

Do not use the critical-angle equation when light travels from lower to higher refractive index, and do not measure the critical angle from the surface rather than the normal.