Refraction is the change in direction of a wave due to a change in its velocity. 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.
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. File:Pencil in a bowl of water.pngRefraction of light waves in water. The dark rectangle represents the actual position of a pencil sitting in a bowl of water. The light rectangle represents the apparent position of the pencil. Notice that the end (X) looks like it is at (Y), a position that is considerably shallower than (X).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, 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. File:Refraction in a ripple tank.pngRefraction of waves in a ripple tankThe 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 colours observed. File:Inferior Image.JPGInferior image formed when light travels from cold air to warm air. The image of the sky appears on the hot ground.While refraction allows for beautiful phenomena such as rainbows it may also produce peculiar optical illusions. A common illusion is a mirage, which occurs when light rays refract as they pass from cold air to warm air. Although 1.0003 is a commonly accepted value for the refractive index of air, the index varies depending on the density of air. Warm air is less dense than cold air and therefore has a lower refractive index. As light passes from colder air to warmer air it bends away from the normal. The diagram on the right shows a light ray coming from the sky toward the hot ground. The air near the ground is warmer and so the light ray bends in a concave up trajectory. Once the ray reaches the viewer’s eye, the eye traces it as the line of sight, which is the line tangent to the path the ray takes at the point it reaches the eye. The result is an inferior image for the above sky appears on the ground. The viewer may incorrectly interpret this sight as water reflecting the sky. File:Refraction.jpgRefraction in a Perspex (acrylic) block.A similar illusion occurs when light travels from warm air to cold air. Light rays traveling in such a path are refracted to produce a superior image in which an object appears above its actual position. An example of this involves cold air above an iceberg. Light rays traveling from warm air toward this cold surface, follow a concave down trajectory. The line of sight traced by the viewer would point up producing such illusions as flying boats.
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 the total refraction phenomena when the wave impedances of the two media are matched. There is no reflected wave.
In medicine, particularly ophthalmology and optometry, refraction (also known as refractometry) is a clinical test for the determination of an 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.  See also: phoropter
Also, since refraction makes 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.