Refractive index

The refractive index is a measure of how much a ray of light bends, or refracts, when it passes through one transparent medium to another. It is also called the index of refraction. It reveals the speed at which the light passes through the medium because the change of speed changes the direction of the light wave. Refraction occurs with any wave, including sound and water. Harnessing the refraction of light waves makes telescopes, magnifying glasses, and prisms possible, and allows the human eye to focus and see.

The law of refraction, which allows one to predict how much the light will bend, is Snell's law. The refractive index is calculated using n=sin i/sin r, in which i is the angle of incidence of a ray in vacuum and r is the angle of refraction. It is also determined by n=c/v, in which c is the speed of light of a given wavelength in empty space and v is its speed in a substance.

Background

Humans have studied the nature of visible light for centuries. Greek philosophers disagreed, although Aristotle was among the first to realize that light travels in waves, much like ripples across the surface of water. By the early eighteenth century, scientists were still at odds over what constitutes light, with some favoring waves and others streams of particles.

Another concern was the speed of light. Galileo attempted to measure the speed of light from one hilltop to another, but light travels too quickly, and means of timing it in the early seventeenth century were too undeveloped. In 1676, Danish astronomer Olaus Roemer observed the eclipses of the moons of Jupiter. He noted that when Earth was moving away from Jupiter, the time between eclipses of the moon Io increased. The opposite was true when Earth was moving closer to Jupiter. He realized the light had to travel farther when the planets were most distant, and he began calculating this difference to predict when the next eclipse would occur. He used the known speed of Earth in orbit to calculate the distance Earth moved between eclipses and estimated the speed of light at 140,000 miles per second. Advances in telescopes and engineering soon gave researchers even more information, and in 1728, British astronomer James Bradley more accurately calculated the speed of light at 185,000 miles per second. His calculations were not far off from the correct speed of 186,000 miles per second.

Seventeenth-century Dutch mathematician Willebrord Snell discovered the law of refraction in 1621, but his work was not published until nearly seventy years after his death. His study built upon the work of Egyptian geographer Ptolemy and Arab scientist Alhazen. Both had attempted to make sense of refraction, with varying degrees of success.

Snell realized that a light traveling into glass in a straight line would not refract, but light entering at an angle would bend. The degree of the refraction is relative to the angle of inclination. Horizontal lines have an angle of inclination of 0 degrees, for example. In 1621, he discovered that every substance has a bending ratio; the refractive index gets higher as the angle of refraction increases.

According to Snell's law, n₁ • sin(θ ₁) = n₂ • sin(θ ₂), in which n represents the refractive indices of material 1 and material 2, while θare the angles of light traveling through them, in reference to normal.

Overview

What humans see as light is waves. The waves are transverse, meaning they vibrate at 90 degrees to the direction in which they travel, and they travel in straight lines. They can travel through air, a vacuum, and through transparent and translucent (not completely clear) substances.

Ray diagrams show how light waves travel. The light rays are drawn as straight lines with a directional arrow. The light traveling toward a substance is the incident ray. A dashed line at 90 degrees to the surface of the substance is called the normal.

The speed at which light travels changes when the waves pass through substances that have different densities. The waves slow down traveling through more dense materials. This change in speed also changes the direction in which the waves travel. This is the refraction of the light waves.

When light goes into a denser substance, the ray slows and bends toward the normal. When light goes into a less dense substance, the ray travels more quickly and bends away from the normal. The absolute index of refraction is the ratio for light passing from a vacuum into a substance. The relative index measures the ratio of the optical densities of two substances, such as water and glass.

The refractive index of air is 1.00, for water it is 1.33, glass is 1.5, and diamond is 2.4. A higher refractive index is an indication that light will slow and change direction more when it enters a substance.

The refractive index is important in a number of industries. For example, in developing electronics, a higher refractive index material can be used to make a much thinner lens. Optical polymers, which are often used for the screens of electronic devices, can be much thinner than glass and correspondingly lighter yet provide the same refractive index. An understanding of the refractive index is necessary when creating lenses, such as magnifying glasses, telescope lenses, and camera lenses. A magnifying glass uses a biconvex lens, also called a converging lens, which is thicker in the middle. This shape focuses parallel rays of light to a focal point. A biconcave lens, which is thinner in the middle, works in the opposite way. It refracts light outward.

Fiber-optic cables also rely on refractive index to function. The cable comprises two layers, the core and the cladding, or outer layer. The core has a greater refractive index of n1, while the cladding has a lesser refractive index of n2. A light ray is injected into the cable at a calculated angle, so that it bounces off the core-to-cladding interface along the cable's length to its destination, where the pulses of light are reassembled by a light-detecting component.

Bibliography

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