Refraction

In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium.^[1] Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed.

Optical prisms and lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the wavelength of light,^[2] and thus the angle of the refraction also varies correspondingly. This is called dispersion and allows certain prisms^[3] and raindrops in rainbows^[4] to divide white light into its constituent spectral colors.

Law

For light, refraction follows Snell's law, which states that, for a given pair of media, the ratio of the sines of the angle of incidence ${\displaystyle {\theta _{1}}}$ and angle of refraction ${\displaystyle {\theta _{2}}}$ is equal to the ratio of phase velocities ${\textstyle {\frac {v_{1}}{v_{2}}}}$ in the two media, or equivalently, to the refractive indices ${\textstyle {\frac {n_{2}}{n_{1}}}}$ of the two media:^[5]

$${\displaystyle {\frac {\sin \theta _{1}}{\sin \theta _{2}}}={\frac {v_{1}}{v_{2}}}={\frac {n_{2}}{n_{1}}}}$$

General explanation

Refraction involves two related parts, both a result of the wave nature of light: a reduced speed in an optical medium and a change in angle when a wave front crosses between different media at an angle.

1. Light slows as it travels through a medium other than vacuum (such as air, glass or water). This is not because of scattering or absorption. Rather it is because, as an electromagnetic oscillation, light itself causes other electrically charged particles such as electrons, to oscillate. The oscillating electrons emit their own electromagnetic waves which interact with the original light. The resulting combined wave has a lower speed. When light returns to a vacuum and there are no electrons nearby, this slowing effect ends and its speed returns to c.
2. When light enters a slower medium at an angle, one side of the wavefront is slowed before the other. This asymmetrical slowing of the light causes it to change the angle of its travel. Once light is within the new medium with constant properties, it travels in a straight line again.

Dispersion of light

Refraction is also responsible for rainbows and for the splitting of white light into a rainbow-spectrum as it passes through a glass prism. Glass and water have higher refractive indices than air. When a beam of white light passes from air into a material having an index of refraction that varies with frequency (and wavelength), a phenomenon known as dispersion occurs, in which different coloured components of the white light are refracted at different angles, i.e., they bend by different amounts at the interface, so that they become separated. The different colors correspond to different frequencies and different wavelengths.

On water

Refraction occurs when light goes through a water surface since water has a refractive index of 1.33 and air has a refractive index of about 1. Looking at a straight object, such as a pencil in the figure here, which is placed at a slant, partially in the water, the object appears to bend at the water's surface. This is due to the bending of light rays as they move from the water to the air. Once the rays reach the eye, the eye traces them back as straight lines (lines of sight). The lines of sight (shown as dashed lines) intersect at a higher position than where the actual rays originated. This causes the pencil to appear higher and the water to appear shallower than it really is.

The depth that the water appears to be when viewed from above is known as the apparent depth. This is an important consideration for spearfishing from the surface because it will make the target fish appear to be in a different place, and the fisher must aim lower to catch the fish. Conversely, an object above the water has a higher apparent height when viewed from below the water. The opposite correction must be made by an archer fish.^[9]

For small angles of incidence (measured from the normal, when sin θ is approximately the same as tan θ), the ratio of apparent to real depth is the ratio of the refractive index of air to that of water. But, as the angle of incidence approaches 90°, the apparent depth approaches zero, albeit reflection increases, which limits observation at high angles of incidence. Conversely, the apparent height approaches infinity as the angle of incidence (from below) increases, but even earlier, as the angle of total internal reflection is approached, albeit the image also fades from view as this limit is approached.

Atmospheric

The refractive index of air depends on the air density and thus vary with air temperature and pressure. Since the pressure is lower at higher altitudes, the refractive index is also lower, causing light rays to refract towards the earth surface when traveling long distances through the atmosphere. This shifts the apparent positions of stars slightly when they are close to the horizon and makes the sun visible before it geometrically rises above the horizon during a sunrise.

Temperature variations in the air can also cause refraction of light. This can be seen as a heat haze when hot and cold air is mixed e.g. over a fire, in engine exhaust, or when opening a window on a cold day. This makes objects viewed through the mixed air appear to shimmer or move around randomly as the hot and cold air moves. This effect is also visible from normal variations in air temperature during a sunny day when using high magnification telephoto lenses and is often limiting the image quality in these cases. ^[10] In a similar way, atmospheric turbulence gives rapidly varying distortions in the images of astronomical telescopes limiting the resolution of terrestrial telescopes not using adaptive optics or other techniques for overcoming these atmospheric distortions.

Air temperature variations close to the surface can give rise to other optical phenomena, such as mirages and Fata Morgana. Most commonly, air heated by a hot road on a sunny day deflects light approaching at a shallow angle towards a viewer. This makes the road appear reflecting, giving an illusion of water covering the road.

In eye care

In medicine, particularly optometry, ophthalmology and orthoptics, refraction (also known as refractometry) is a clinical test in which a phoropter may be used by the appropriate eye care professional to determine the eye's refractive error and the best corrective lenses to be prescribed. A series of test lenses in graded optical powers or focal lengths are presented to determine which provides the sharpest, clearest vision.^[11] Refractive surgery is a medical procedure to treat common vision disorders.

Mechanical waves

Water

Main article: Water wave refraction

Water waves travel slower in shallower water. This can be used to demonstrate refraction in ripple tanks and also explains why waves on a shoreline tend to strike the shore close to a perpendicular angle. As the waves travel from deep water into shallower water near the shore, they are refracted from their original direction of travel to an angle more normal to the shoreline.^[12]

Gallery

See also

• Birefringence (double refraction)
• Geometrical optics
• Huygens–Fresnel principle
• List of indices of refraction
• Negative refraction
• Reflection
• Schlieren photography
• Seismic refraction
• Super refraction

References

External links

Wikimedia Commons has media related to Refraction.

• Reflections and Refractions in Ray Tracing, a simple but thorough discussion of the mathematics behind refraction and reflection.
• Flash refraction simulation- includes source, Explains refraction and Snell's Law.
• "Refraction" . Encyclopædia Britannica. Vol. 23 (11th ed.). 1911. pp. 25–29.