refract

Refract is the change in direction of a wave as it passes from one medium to another with a different propagation speed. The phenomenon is most familiar for light, but it also affects sound, water waves, and other disturbances. Refraction is governed by the refractive index of each medium, a dimensionless measure of how fast waves propagate there.

When a wave crosses an interface, its speed changes, causing the path to bend. For light, Snell's law relates the incident angle theta1 and the refracted angle theta2 to the refractive indices n1 and n2: n1 sin(theta1) = n2 sin(theta2). If n2 > n1, the ray bends toward the normal; if n2 < n1, it bends away from the normal. The frequency remains constant, but the wavelength changes as light enters a different medium.

The dependence of the refractive index on wavelength, or dispersion, explains why prisms split white light into a spectrum. Refraction also explains atmospheric effects such as the apparent flattening or lifting of celestial bodies near the horizon, and the creation of mirages.

In denser media, light may undergo total internal reflection when the incidence angle exceeds a critical angle given by sin(theta_c) = n2/n1. This principle underlies optical fibers and endoscopes, which rely on internal reflection to guide light along long distances.

Applications and related concepts include lenses in eyeglasses and cameras that focus light, prisms that disperse light, gradient-index optics where the refractive index varies gradually to bend light smoothly, and refractive techniques in ultrasound and seismic imaging for subsurface investigations.