Optics/Refraction



Refraction is the change in direction and phase velocity of a wave due to a change in the medium in which the wave is traveling. A wave which undergoes this phenomenon is said to have been refracted. This phenomenon is most commonly observed when a wave passes from one medium to another at any angle other than 90° or 0°. Refraction is described by Snell's law (also known as the Snell–Descartes law and the law of refraction), which states that for a given pair of media and a wave with a single frequency, the ratio of the sines of the angle of incidence $$\theta_1$$ and angle of refraction $$\theta_2$$ is equivalent to the ratio of phase velocities $$v_1 \over v_2$$ in the two media, or equivalently, to the opposite ratio of the indices of refraction $$n_2 \over n_1$$:
 * $$\frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2} = \frac{n_2}{n_1} .$$

When a wave travels across an interface and into a medium with a higher index of refraction, the wave bends towards the normal. If a wave travels across an interface and into a lower index of refraction, the wave bends away from the normal. If a wave travels across an interface and into a medium with the same index of refraction, the direction of the wave's propagation does not change. The two most common indices of refraction used when first exploring the topic of refraction are air ($$n=1.00029$$) and water ($$n=1.33$$). To simplify calculations, the index of refraction of air is typically approximated to be $$n=1.00$$ (which is actually the index of refraction of a vacuum).

As the angle of incidence increases, the angle of refraction also increases. There comes a point in which the angle of refraction is 90° and means that the wave refracts parallel to the interface. This angle is called the critical angle and for angles greater than or equal to the critical angle, refraction does not take place and all of the light is reflected; this phenomenon is called total internal reflection and will be covered in the next section.