Definitions

# refraction

[ri-frak-shuhn]
refraction, in physics, deflection of a wave on passing obliquely from one transparent medium into a second medium in which its speed is different, as the passage of a light ray from air into glass. Other forms of electromagnetic radiation, in addition to light waves, can be refracted, as can sound waves.

## The Nature of Refraction

Refraction is commonly explained in terms of the wave theory of light and is based on the fact that light travels with greater velocity in some media than it does in others. When, for example, a ray of light traveling through air strikes the surface of a piece of glass at an oblique angle, one side of the wave front enters the glass before the other and is retarded (since light travels more slowly in glass than in air), while the other side continues to move at its original speed until it too reaches the glass. As a result, the ray bends inside the glass, i.e., the refracted ray lies in a direction closer to the normal (the perpendicular to the boundary of the media) than does the incident ray. A light ray entering a different medium is called the incident ray; after bending, the ray is called the refracted ray. The speed at which a given transparent medium transmits light waves is related to its optical density (not to be confused with mass or weight density). In general, a ray is refracted toward the normal when it passes into a denser medium and away from the normal when it passes into a less dense medium.

## The Law of Refraction

The law of refraction relates the angle of incidence (angle between the incident ray and the normal) to the angle of refraction (angle between the refracted ray and the normal). This law, credited to Willebrord Snell, states that the ratio of the sine of the angle of incidence, i, to the sine of the angle of refraction, r, is equal to the ratio of the speed of light in the original medium, vi, to the speed of light in the refracting medium, vr, or sin i/sin r=vi/vr. Snell's law is often stated in terms of the indexes of refraction of the two media rather than the speeds of light in the media. The index of refraction, n, of a transparent medium is a direct measure of its optical density and is equal to the ratio of the speed of light in a vacuum, c, to the speed of light in the medium: n=c/v.

Indexes of refraction are always equal to or greater than 1; for air, n=1.00029; for water, n=1.33. Using indexes of refraction, Snell's law takes the form sin i/sin r=nr /ni, or ni sin i=nr sin r. If the original medium is denser than the refracting medium (ni greater than nr), sin r will be greater than sin i. Thus, there will be some acute angle less than 90° for the incident ray corresponding to an angle of refraction of 90°. This angle of incidence is known as the critical angle. For angles of incidence greater than the critical angle, refraction cannot take place and the incident ray is instead reflected back into the original medium according to the law of reflection (angle of reflection equals angle of incidence). This phenomenon is known as total internal reflection.

## Applications of Refraction

Refraction has many applications in optics and technology. A lens uses refraction to form an image of an object for many different purposes, such as magnification. A prism uses refraction to form a spectrum of colors from an incident beam of light. Refraction also plays an important role in the formation of a mirage and other optical illusions.

Change in direction of a wave as it leaves one medium and enters another. Waves, such as sound and light waves, travel at different speeds in different media. When a wave enters a new medium at an angle of less than 90°, the change in speed occurs sooner on one side of the wave than on the other, causing the wave to bend, or refract. When water waves approach shallower water at an angle, they bend and become parallel to the shore. Refraction explains the apparent bending of a pencil when it is partly immersed in water and viewed from above the surface. It also causes the optical illusion of the mirage.

or birefringence

Optical property in which a single ray of unpolarized light (see polarization) splits into two components traveling at different velocities and in different directions. One ray is refracted (see refraction) at an angle as it travels through the medium, while the other passes through unchanged. The splitting occurs because the speed of the ray through the medium is determined by the orientation of the light compared with the crystal lattice of the medium. Since unpolarized light consists of waves that vibrate in all directions, some will pass through the lattice without being affected, while others will be refracted and change direction. Materials that exhibit double refraction include ice, quartz, and sugar.

Refraction is the change in direction of a wave due to a change in its speed. This is most commonly seen when a wave passes from one medium to another. Refraction of light is the most commonly seen example, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium into another or when water waves move into water of a different depth. Refraction is described by Snell's law, which states that the angle of incidence is related to the angle of refraction by

$frac\left\{sintheta_1\right\}\left\{sintheta_2\right\} = frac\left\{v_1\right\}\left\{v_2\right\} = frac\left\{n_2\right\}\left\{n_1\right\}$
or
$n_1sintheta_1 = n_2sintheta_2$
where
$v_1$ and $v_2$ are the wave velocities through the respective media.
$theta_1$ and $theta_2$ are the angles between the normal (to the interface) plane and the incident waves respectively.
$n_1$ and $n_2$ are the refractive indices

## Explanation

In optics, refraction occurs when light waves travel from a medium with a given refractive index to a medium with another. At the boundary between the media, the wave's phase velocity is altered, it changes direction, and its wavelength increases or decreases but its frequency remains constant. For example, a light ray will refract as it enters and leaves glass; understanding of this concept led to the invention of lenses and the refracting telescope.

In History, Ibn Sahl is credited with first discovering the law of refraction, usually called Snell's law. He used the law of refraction to work out the shapes of lenses that focus light with no geometric aberrations, known as anaclastic lenses. Seen http://en.wikipedia.org/wiki/Ibn_Sahl ; Ibn Sahl (Abu Sa`d al-`Ala' ibn Sahl) (c. 940-1000) was an Muslim Arabian mathematician, physicist and optics engineer associated with the Abbasid court of Baghdad. About 984 he wrote a treatise On Burning Mirrors and Lenses in which he set out his understanding of how curved mirrors and lenses bend and focus light.

Refraction can be seen when looking into a bowl of water. Air has a refractive index of about 1.0003, and water has a refractive index of about 1.33. If a person looks at a straight object, such as a pencil or straw, 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.

The diagram on the right shows an example of refraction in water waves. Ripples travel from the left and pass over a shallower region inclined at an angle to the wavefront. The waves travel more slowly in the shallower water, so the wavelength decreases and the wave bends at the boundary. The dotted line represents the normal to the boundary. The dashed line represents the original direction of the waves. The phenomenon explains why waves on a shoreline never hit the shoreline at an angle. Whichever direction the waves travel in deep water, they always refract towards the normal as they enter the shallower water near the beach.

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 has a higher refractive index than air and the different frequencies of light travel at different speeds (dispersion), causing them to be refracted at different angles, so that you can see them. The different frequencies correspond to different colors observed.

While refraction allows for beautiful phenomena such as rainbows, it may also produce peculiar optical phenomena, such as mirages and Fata Morgana. These are caused by the change of the refractive index of air with temperature.

Snell's law is used to calculate the degree to which light is refracted when traveling from one medium to another.

Recently some metamaterials have been created which have a negative refractive index. With metamaterials, we can also obtain total refraction phenomena when the wave impedances of the two media are matched. There is no reflected wave.

Also, since refraction can make objects appear closer than they are, it is responsible for allowing water to magnify objects. First, as light is entering a drop of water, it slows down. If the water's surface is not flat, then the light will be bent into a new path. This round shape will bend the light outwards and as it spreads out, the image you see gets larger.

A useful analogy in explaining the refraction of light would be to imagine a marching band as they march from pavement (a fast medium) into mud (a slower medium) The marchers on the side that runs into the mud first will slow down first. This causes the whole band to pivot slightly toward the normal (make a smaller angle from the normal).

## Optometry

In medicine, particularly optometry and ophthalmology, refraction (also known as refractometry) is a clinical test in which a phoropter may used by an optometrist 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 provide the sharpest, clearest vision.

## Acoustics

In underwater acoustics, refraction is the bending or curving of a sound ray that results when the ray passes through a sound speed gradient from a region of one sound speed to a region of a different speed. The amount of ray bending is dependent upon the amount of difference between sound speeds, that is, the variation in temperature, salinity, and pressure of the water. Similar acoustics effects are also found in the Earth's atmosphere. The phenomenon of refraction of sound in the atmosphere has been known for centuries; however, beginning in the early 1970s, widespread analysis of this effect came into vogue through the designing of urban highways and noise barriers to address the meteorological effects of bending of sound rays in the lower atmosphere.