Snell's Law

Refraction is the change of direction of light rays between two different media. If the speed of light is different in two media (v₁ and v₂), then the angle of refraction, $\theta$₂, is given from the incident angle, $\theta$₁, by Snell's Law:

\[ \rm \mathbf{ \frac{sin \theta_{1}}{sin \theta_{2}} = \frac{v_{1}}{v_{2}}} \]

Proof:

We consider the two blue right triangles. The lengths d₁ and d₂ are given by: d₁ = v₁ $\Delta$t and d₂ = v₂ $\Delta$t
with the same $\Delta$t.
Dividing these two equations by each other results in:
(i) \[ \rm \mathbf{ \frac{d_{1}}{d_{2}} = \frac{v_{1}}{v_{2}}} \]
On the other hand, we get from trigonometry: \[ \rm \mathbf{ \frac{d_{1}}{L} = sin \theta_{1} and \frac{d_{2}}{L} = sin \theta_{2} \Rightarrow } \]
(ii) \[ \rm \mathbf{ \frac{d_{1}}{d_{2}} = \frac{sin \theta_{1}}{sin \theta_{2}}} \]
Combining equations (i) and (ii) gives the desired result.