Refraction

Refraction is the change in direction of a wave as it enters a medium with a different propagation speed or travels through a medium whose properties vary continuously. It is especially familiar in optics, where light bends between air, glass, and water, making submerged objects appear displaced and enabling lenses to form images. Refraction differs from reflection, in which a wave returns into the incident medium. At a boundary, both phenomena may occur simultaneously. (openstax.org)

Refractive index and wave propagation

For light, the refractive index $n$ is defined by

where $c$ is the speed of light in vacuum and $v_{\mathrm p}$ is the phase velocity in the material—the speed at which a surface of constant wave phase advances. For visible light under ordinary conditions, air has an index close to 1, water approximately 1.33, and many common glasses approximately 1.5. These values depend on wavelength and material conditions. (openstax.org)

When a monochromatic wave crosses a stationary interface between ordinary, linear media, its frequency remains unchanged. Its speed and wavelength change together, according to $v_{\mathrm p}=f\lambda$. A shorter wavelength inside glass therefore does not imply that the light has acquired a different frequency. The direction changes because wavefronts advance at different speeds on the two sides of the interface. (feynmanlectures.caltech.edu)

Microscopically, an incident electric field drives charged constituents of matter into motion. Their radiation combines with the incident wave through interference, producing a phase shift that accumulates with distance. This collective electromagnetic response explains the effective propagation speed; it is not simply a sequence of independent absorption events followed by delayed re-emission. (feynmanlectures.caltech.edu)

Snell’s law

At a smooth boundary between two homogeneous, isotropic media, refraction obeys Snell’s law:

Here $n_1$ and $n_2$ are the refractive indices, and $\theta_1$ and $\theta_2$ are the incident and refracted angles. Both angles are measured from the normal, the line perpendicular to the boundary, rather than from the surface itself. The incident ray, refracted ray, and normal lie in one plane. (openstax.org)

For positive refractive indices, light entering a higher-index medium bends toward the normal; light entering a lower-index medium bends away from it. At normal incidence, no directional bending occurs, although speed and wavelength can still change. Thus, refraction should not be interpreted as requiring a visibly bent path in every case. (openstax.org)

The law follows from the matching of wave phase along the interface. It can also be derived from Fermat’s principle, which states that the optical travel time is stationary with respect to small variations of the path. “Stationary” is more general than “shortest”: the familiar least-time formulation describes many elementary situations but is not the most general statement. (feynmanlectures.caltech.edu)

Total internal reflection

When light travels from a higher-index medium into a lower-index one, increasing the incident angle eventually makes the refracted ray parallel to the boundary. This defines the critical angle:

Above this angle, no propagating transmitted ray exists in the second medium. For an ideal interface between lossless media, the incident light undergoes total internal reflection. For water adjoining air, the critical angle is approximately $48.6^\circ$. (openstax.org)

This behavior confines light in optical fibers, whose core has a higher refractive index than the surrounding cladding. It also allows appropriately shaped prisms to redirect light without a metallic reflecting coating. Total internal reflection is therefore a consequence of the conditions governing refraction, rather than an unrelated optical effect. (openstax.org)

Dispersion and polarization

The refractive index generally depends on frequency. This dependence is called dispersion. A prism separates white light because different wavelengths emerge at different angles. In the normal-dispersion region of many transparent materials, shorter visible wavelengths have a higher index and are deflected more strongly than longer wavelengths. Rainbows combine dispersion with refraction on entering and leaving water droplets and reflection within them. (openstax.org)

Refraction can also depend on polarization. In anisotropic materials, the optical response varies with direction. Some crystals exhibit birefringence, splitting an incident beam into two modes with different propagation properties. Consequently, the simple picture of one refracted ray governed by one direction-independent index is insufficient for such materials. (feynmanlectures.caltech.edu)

Image formation and atmospheric effects

A lens uses refraction at shaped surfaces to make rays converge or diverge. Its optical behavior depends on surface curvature and the refractive index relative to the surrounding medium. A converging lens can form a real image where rays meet, or a virtual image where their backward extensions meet. Refraction underlies the operation of cameras, magnifying glasses, refracting telescopes, and many microscopes. (openstax.org)

Refraction need not occur at a sharp boundary. Within the atmosphere, gradual variations in refractive index produce curved propagation paths. Changes in atmospheric structure can bend radar beams more or less than usual. Strong downward bending may cause a beam to encounter the ground, generating echoes that can be mistaken for precipitation unless their origin is recognized. (noaa.gov)