Refraction

As the light travels through the air, it is suddenly confronted with a new obstacle: a pane of glass. The light, being a wave, is forced to change its course as it enters this new medium. This phenomenon, known as refraction, occurs whenever a wave passes from one medium to another and is caused by the wave's change in speed or the change in the medium itself.

Snell's law describes how much a wave, such as light, is refracted as it travels through different media. This law states that the ratio of the sines of the angle of incidence and the angle of refraction is equal to the ratio of the phase velocities in the two media, or the refractive indices of the two media.

Optical devices such as prisms and lenses utilize refraction to redirect light, and the human eye also relies on this effect. The refractive index of materials can vary depending on the wavelength of light, leading to a corresponding change in the angle of refraction. This effect, known as dispersion, causes white light to be divided into its spectral colors when it passes through a prism or raindrops in the air.

Refraction is a phenomenon that affects light waves as they pass through different mediums, altering their direction of travel. It is an important aspect of our everyday life and is at the heart of various optical devices such as glasses, cameras, and microscopes.

This phenomenon can also be observed in natural optical phenomena like rainbows and mirages. To understand refraction, it is important to consider the wave nature of light and the fact that it slows down as it travels through a medium other than a vacuum, such as air or glass. This slowing is not due to absorption or scattering, but rather because the light wave causes other charged particles like electrons to oscillate, emitting their own electromagnetic waves that interact with the original light. The resulting combined wave has wave packets that pass an observer at a slower rate, effectively slowing the light.

When light enters a medium at an angle, it slows asymmetrically, causing it to change its angle of travel. Once it is within a medium with constant properties, it travels in a straight line again.

As previously mentioned, light waves slow down as they pass through a medium other than a vacuum. This is the cause of phenomena like refraction, and when light returns to a vacuum, it resumes its usual speed of c, ignoring any gravitational effects.

Contrary to popular belief, the slowing of light is not due to scattering or absorption by atoms. These explanations would cause a blurring effect in the light as it would no longer be traveling in a single direction, but this effect is not observed in nature.

The true cause of the slowing of light lies in its nature as an electromagnetic wave. When light travels through a medium, it causes the material's electrically charged electrons to oscillate. These oscillating electrons emit their own electromagnetic waves that interact with the original light waves, similar to the way water waves interact on a pond. This process, known as constructive interference, results in a combined wave that may have wave packets that pass an observer at a slower rate, effectively slowing the light. When the light leaves the medium, this interaction with electrons no longer occurs and the wave packet rate, and therefore the speed, returns to normal.

Imagine a wave traveling from one material to another where its speed is slower, as shown in the figure. When it reaches the interface between the two materials at an angle, one side of the wave will reach the second material first and slow down earlier. This causes the whole wave to pivot towards the side that is slowed down. This is why a wave will bend away from the surface or towards the normal when it enters a slower material. On the other hand, if a wave reaches a material where its speed is higher, one side of the wave will speed up and the wave will pivot away from that side.

Another way to understand this phenomenon is to consider the change in wavelength at the interface. When a wave goes from one material to another where its speed is different, the frequency of the wave will remain the same, but the distance between wavefronts, or wavelength, will change. If the speed is decreased, as shown in the figure, the wavelength will also decrease. The angle between the wavefronts and the interface must change to keep the wavefronts intact, given the change in distance between them. From these considerations, the relationship between the angle of incidence, angle of transmission, and the wave speeds in the two materials can be derived, resulting in the law of refraction, also known as Snell's law.

In a more fundamental sense, the phenomenon of refraction can be derived from the two- or three-dimensional wave equation. The boundary condition at the interface requires the tangential component of the wave vector to be identical on both sides of the interface. Since the magnitude of the wave vector depends on the wave speed, this requires a change in the direction of the wave vector.

It is important to note that the relevant wave speed in this context is the phase velocity of the wave, which is typically close to the group velocity, but may differ in certain cases. The group velocity can be thought of as the true speed of a wave, but the phase velocity should be used in all calculations related to refraction. A wave traveling perpendicular to a boundary, with its wavefronts parallel to the boundary, will not change direction even if its speed changes.

Light refraction occurs when it passes through the surface of water, as water has a refractive index of 1.33 and air has a refractive index of about 1. If you look at a straight object, such as a pencil, placed at an angle partially in the water, the object appears to bend at the water's surface. This is because the light rays bend as they move from the water to the air, and when they reach the eye, the eye traces them back as straight lines (lines of sight). These lines of sight intersect at a higher position than where the actual rays originated, causing 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 because it will make the target fish appear to be in a different location, requiring the fisher to aim lower to catch the fish. Similarly, an object above the water appears to be at a higher apparent height when viewed from below the water. An archer fish must take this into account and aim accordingly.

For small angles of incidence, the ratio of apparent to real depth is the ratio of the refractive indexes of air to water. However, as the angle of incidence approaches 90 degrees, the apparent depth approaches zero, although reflection increases, limiting observation at high angles of incidence. Similarly, 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, although the image also fades from view as this limit is approached.

Refraction is also the cause of rainbows and 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 when white light passes from air into a material with a refractive index that varies with frequency, a phenomenon known as dispersion occurs. During dispersion, different colored components of the white light are refracted at different angles, meaning they bend by different amounts at the interface and become separated. These different colors correspond to different frequencies.

The refractive index of air depends on the air density and can vary with air temperature and pressure. At higher altitudes, the pressure is lower, causing the refractive index to also be lower and light rays to refract towards the Earth's 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 rises above the horizon during a sunrise.

Temperature variations in the air can also cause refraction of light, resulting in a heat haze when hot and cold air is mixed. This can be seen over a fire, in engine exhaust, or when opening a window on a cold day and 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 temperature variations in the air on a sunny day when using high magnification telephoto lenses and can limit image quality in these cases.

Atmospheric turbulence can also cause rapidly varying distortions in the images of astronomical telescopes, limiting the resolution of terrestrial telescopes that do not use adaptive optics or other techniques to overcome these atmospheric distortions.

Temperature variations close to the surface can give rise to other optical phenomena like mirages and Fata Morgana. Often, air heated by a hot road on a sunny day deflects light approaching at a shallow angle towards a viewer, making the road appear reflective and creating the illusion of water covering it.

In the field of medicine, particularly in optometry, ophthalmology, and orthoptics, refraction is a clinical test used by eye care professionals to determine the refractive error of the eye and the best corrective lenses to be prescribed. This test involves the use of a phoropter, which presents a series of test lenses in graded optical powers or focal lengths to determine which provides the sharpest, clearest vision.

Refraction can also be demonstrated through the use of ripple tanks, which show that water waves travel slower in shallower water. This same principle explains why waves on a shoreline tend to hit the shore at 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.

In underwater acoustics, refraction is the bending or curving of a sound ray that occurs when it passes through a sound speed gradient from a region with one sound speed to a region with a different speed. The amount of ray bending depends on the difference in sound speeds, which can be caused by variations in temperature, salinity, and pressure of the water. Similar acoustics effects can also be found in the Earth's atmosphere, where refraction of sound has been known for centuries. In the early 1970s, widespread analysis of this effect became popular through the design of urban highways and noise barriers to address the meteorological effects of bending sound rays in the lower atmosphere.