How Big is the Critical Angle Here?

The index of refraction for polystyrene is found to be 1.49 in Figure 25.14, and the index of refraction of air can be taken to be 1.00, as before. Thus, the condition that the second medium (air) has an index of refraction less than the first (plastic) is satisfied, and the equation ${\theta }_c={\text{sin}}^{-1}\left(n_2/n_1\right)$ can be used to find the critical angle ${\theta }_c$. Here, then, $n_2=1\text{.}\text{00}$ and $n_1=1\text{.}\text{49}$.

The critical angle is given by

Substituting the identified values gives

This means that any ray of light inside the plastic that strikes the surface at an angle greater than $\text{42.2º}$ will be totally reflected. This will make the inside surface of the clear plastic a perfect mirror for such rays without any need for the silvering used on common mirrors. Different combinations of materials have different critical angles, but any combination with $n_1>n_2$ can produce total internal reflection. The same calculation as made here shows that the critical angle for a ray going from water to air is $\text{48}\text{.}\mathrm{6º}$, while that from diamond to air is $\text{24}\text{.}\mathrm{4º}$, and that from flint glass to crown glass is $\text{66}\text{.}\mathrm{3º}$. There is no total reflection for rays going in the other direction—for example, from air to water—since the condition that the second medium must have a smaller index of refraction is not satisfied. A number of interesting applications of total internal reflection follow.