Refraction is the change in direction and usually the speed of a wave when it passes from one medium or propagation region into another in which its phase velocity is different. The phenomenon is commonly demonstrated with light passing from air into glass or water, but refraction also occurs for sound, water waves and other types of waves.
When a wave crosses a boundary obliquely and its speed changes, different parts of the wavefront reach the new medium at different times, causing the wavefront to rotate and the propagation direction to change. The frequency of a steady wave does not normally change merely because the wave crosses a stationary boundary. Instead, the wavelength changes in proportion to the change in wave speed, because wave speed equals frequency multiplied by wavelength. Refraction is therefore fundamentally connected with differences in propagation speed and boundary geometry, rather than with a wave simply changing direction for no physical reason.
For light, refraction is commonly described using refractive index. The refractive index of a medium is related to the speed of light in vacuum divided by the phase velocity of light in that medium, although the detailed interpretation can depend on frequency and material dispersion.
Snells law gives the relationship between incident and refracted angles in an ideal interface, expressed as n1 sin theta1 equals n2 sin theta2, where n1 and n2 are the refractive indices and theta1 and theta2 are measured from the normal to the boundary. If light enters a medium with a larger refractive index, its phase velocity decreases and the ray bends towards the normal for oblique incidence. If it enters a lower refractive index medium, it bends away from the normal. At normal incidence there is no directional bending, although the speed and wavelength can still change.
Refraction does not mean that every wave changes direction whenever its speed changes. Directional bending requires an appropriate geometry, such as oblique incidence or a spatially varying propagation speed. If a wave enters a new medium perpendicular to the boundary, its direction remains along the normal, even though its speed and wavelength change. Refraction can also occur gradually rather than at a sharp boundary.
In a medium whose refractive index varies continuously across space, wavefronts can curve continuously and rays can follow curved trajectories. Atmospheric refraction is an important example because temperature, pressure and humidity variations change the refractive properties of air with altitude. Light travelling through such layers can follow curved paths, contributing to effects such as mirages and changes in the apparent position of distant objects.
The physical explanation of refraction can be expressed through wavefront geometry and the principle of stationary optical path. In wavefront descriptions, the portion of a wavefront entering the new medium first changes speed while the remainder continues at the original speed. The resulting difference in travel rate rotates the wavefront, and the propagation direction, which is perpendicular to the wavefront in an isotropic medium, changes accordingly.
Fermats principle provides another formulation for geometrical optics by stating that the actual optical path between specified points is stationary with respect to small variations in the path. This principle leads to Snells law when applied to an interface between two homogeneous media. The two descriptions are mathematically connected and illustrate that refraction is a consequence of the way wave propagation interacts with spatially varying material properties.
Dispersion is a related phenomenon in which the propagation properties of a material depend on frequency or wavelength. Because different wavelengths of light can have different refractive indices in a material, white light entering a prism can be separated into its component colours. Violet light and red light generally experience different amounts of refraction in ordinary transparent materials because their phase velocities differ.
This wavelength dependence is responsible for the formation of spectra from prisms and contributes to chromatic aberration in lenses. Dispersion can be normal or anomalous depending on the frequency range and material response. The simple refractive index used in introductory optics therefore represents only part of the complete electromagnetic response of a material. At more advanced levels, refraction is described using frequency dependent complex optical properties, particularly when absorption and other forms of dispersion are significant.
Refraction is important in many technologies. Lenses rely on refraction to converge or diverge light and thereby form images. Cameras, microscopes, telescopes, spectacles, projectors and many optical instruments use carefully shaped refracting surfaces. Fibre optic communication relies primarily on guided propagation and total internal reflection, but refractive index determines the optical behaviour at the fibre boundaries and is central to how the guide operates. In atmospheric science, refraction affects astronomical observations, radar propagation and the apparent positions of objects.
In acoustics, changes in temperature or wind speed can refract sound, causing sound to bend towards regions where its propagation speed is lower under appropriate conditions. In medical imaging, ultrasound propagation depends on differences in acoustic properties between tissues, and refraction can affect the paths of ultrasound beams at interfaces.
Refraction is distinct from reflection even though both occur at boundaries. When a wave encounters an interface, part of its energy can be transmitted into the second medium and part can be reflected back into the first, depending on the wave and boundary properties. The transmitted component can refract, while the reflected component follows reflection laws. Refraction is also distinct from diffraction.
Diffraction results from wave interaction with apertures, obstacles or spatial constraints and involves spreading and interference, whereas ordinary refraction at an interface primarily results from a change in propagation speed between regions. Scattering is another related but distinct process involving redistribution of waves by particles, irregularities or structures. In real materials these effects can occur simultaneously, making experimental interpretation dependent on geometry, wavelength and material properties.
Several common misconceptions arise from treating refraction as a change in frequency or as a universal property of a particular material independent of wavelength and conditions. The frequency of a wave crossing a stationary boundary generally remains continuous across the boundary because the oscillation rate must match at the interface, while the speed and wavelength change. Refractive index can also vary with wavelength, temperature, pressure, composition and direction in anisotropic materials.
In anisotropic crystals, the relationship between wave direction, energy flow and refractive index can be more complicated than the simple isotropic model. Refraction is consequently a general wave phenomenon whose simplest textbook description is based on a sharp boundary between homogeneous isotropic media, while real applications often require detailed treatment of material dispersion, anisotropy, absorption, geometry and wave polarisation.
