Refraction and Snell's law

When light passes from one medium to another — for example from air to glass — it changes speed and, if the angle of incidence is not zero, it also changes direction. This is the phenomenon of refraction. The deviation is governed by the refractive indices of the two media and by the angles, always measured from the normal.

Principle — Snell's law

If a ray passes from a medium with index $n_1$ to one with index $n_2$: $\ev{n_1\,\sin\theta_1 = n_2\,\sin\theta_2}$

The refractive index of a medium is $n = c/v$, where $v$ is the speed of light in the medium: it equals $n = 1$ in a vacuum, $n \approx 1{,}33$ in water and $n \approx 1{,}5$ in glass. Since light is slower in glass, when passing from air to glass the ray bends towards the normal; in the reverse passage it bends away from it.

Passing from air to the denser glass, the refracted ray bends towards the normal: $\theta_2 < \theta_1$.

Total internal reflection: the "sine greater than 1"

What happens if light is made to pass from a dense medium to a less dense one (water $\to$ air) at a very steep angle? The formula $\sin\theta_2 = (n_1/n_2)\sin\theta_1$ can give $\sin\theta_2 > 1$, which is impossible. Nature resolves the paradox in spectacular fashion: the ray does not refract, it is entirely reflected back into the dense medium. This is total internal reflection, the principle behind optical fibres, where light stays trapped and travels for kilometres bouncing off the walls. The critical angle $\theta_c$, beyond which total reflection begins, is $\sin\theta_c = \frac{n_2}{n_1}$ For water $\to$ air, $\theta_c \approx 48^\circ$.

Collegamenti

Argomenti: Ottica Concetti: Rifrazione e legge di Snell

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