Light

IV

Measuring Light

Monochromatic light, or light of one color, has several characteristics that can be measured. As discussed in the section on electromagnetic waves, the length of light waves is measured in meters, and the frequency of light waves is measured in hertz. The wavelength can be measured with interferometers, and the frequency determined from the wavelength and a measurement of the velocity of light in meters per second. Monochromatic light also has a well-defined polarization that can be measured using devices called polarimeters. Sometimes the direction of scattered light is also an important quantity to measure.

When light is considered as a source of illumination for human eyes, its intensity, or brightness, is measured in units that are based on a modernized version of the perceived brightness of a candle. These units include the rate of energy flow in light, which, for monochromatic light traveling in a single direction, is determined by the rate of flow of photons. The rate of energy flow in this case can be stated in watts, or Joules per second. Usually light contains many colors and radiates in many directions away from a source such as a lamp.

A

Brightness

Scientists use the units candela and lumen to measure the brightness of light as perceived by humans. These units account for the different response of the eye to light of different colors. The lumen measures the total amount of energy in the light radiated in all directions, and the candela measures the amount radiated in a particular direction. The candela was originally called the candle, and it was defined in terms of the light produced by a standard candle. It is now defined as the energy flow in a given direction of a yellow-green light with a frequency of 540 x 10¹² Hz and a radiant intensity, or energy output, of 1/683 watt into the opening of a cone of one steradian. The steradian is a measure of angle in three dimensions.

The lumen can be defined in terms of a source that radiates one candela uniformly in all directions. If a sphere with a radius of one foot were centered on the light source, then one square foot of the inside surface of the sphere would be illuminated with a flux of one lumen. Flux means the rate at which light energy is falling on the surface. The illumination, or luminance, of that one square foot is defined to be one foot-candle.

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The illumination at a different distance from a source can be calculated from the inverse square law: One lumen of flux spreads out over an area that increases as the square of the distance from the center of the source. This means that the light per square foot decreases as the inverse square of the distance from the source. For instance, if 1 square foot of a surface that is 1 foot away from a source has an illumination of 1 foot-candle, then 1 square foot of a surface that is 4 feet away will have an illumination of 1/16 foot-candle. This is because 4 feet away from the source, the 1 lumen of flux landing on 1 square foot has had to spread out over 16 square feet. In the metric system, the unit of luminous flux is also called the lumen, and the unit of illumination is defined in meters and is called the lux.

B

The Speed of Light

Scientists have defined the speed of light in a vacuum to be exactly 299,792,458 meters per second (about 186,000 miles per second). This definition is possible because since 1983, scientists have known the distance light travels in one second more accurately than the definition of the standard meter. Therefore, in 1983, scientists defined the meter as 1/299,792,458, the distance light travels through a vacuum in one second. This precise measurement is the latest step in a long history of measurement, beginning in the early 1600s with an unsuccessful attempt by Italian scientist Galileo to measure the speed of lantern light from one hilltop to another.

The first successful measurements of the speed of light were astronomical. In 1676 Danish astronomer Olaus Roemer noticed a delay in the eclipse of a moon of Jupiter when it was viewed from the far side as compared with the near side of Earth’s orbit. Assuming the delay was the travel time of light across Earth’s orbit, and knowing roughly the orbital size from other observations, he divided distance by time to estimate the speed.

English physicist James Bradley obtained a better measurement in 1729. Bradley found it necessary to keep changing the tilt of his telescope to catch the light from stars as Earth went around the Sun. He concluded that Earth’s motion was sweeping the telescope sideways relative to the light that was coming down the telescope. The angle of tilt, called the stellar aberration, is approximately the ratio of the orbital speed of Earth to the speed of light. (This is one of the ways scientists determined that Earth moves around the Sun and not vice versa.)

In the mid-19th century, French physicist Armand Fizeau directly measured the speed of light by sending a narrow beam of light between gear teeth in the edge of a rotating wheel. The beam then traveled a long distance to a mirror and came back to the wheel where, if the spin were fast enough, a tooth would block the light. Knowing the distance to the mirror and the speed of the wheel, Fizeau could calculate the speed of light. During the same period, the French physicist Jean Foucault made other, more accurate experiments of this sort with spinning mirrors.

Scientists needed accurate measurements of the speed of light because they were looking for the medium that light traveled in. They called the medium ether, which they believed waved to produce the light. If ether existed, then the speed of light should appear larger or smaller depending on whether the person measuring it was moving toward or away from the ether waves. However, all measurements of the speed of light in different moving reference frames gave the same value.

In 1887 American physicists Albert A. Michelson and Edward Morley performed a very sensitive experiment designed to detect the effects of ether. They constructed an interferometer with two light beams—one that pointed along the direction of Earth’s motion, and one that pointed in a direction perpendicular to Earth’s motion. The beams were reflected by mirrors at the ends of their paths and returned to a common point where they could interfere. Along the first beam, the scientists expected Earth’s motion to increase or decrease the beam’s velocity so that the number of wave cycles throughout the path would be changed slightly relative to the second beam, resulting in a characteristic interference pattern. Knowing the velocity of Earth, it was possible to predict the change in the number of cycles and the resulting interference pattern that would be observed. The Michelson-Morley apparatus was fully capable of measuring it, but the scientists did not find the expected results.

The paradox of the constancy of the speed of light created a major problem for physical theory that German-born American physicist Albert Einstein finally resolved in 1905. Einstein suggested that physical theories should not depend on the state of motion of the observer. Instead, Einstein said the speed of light had to remain constant, and all the rest of physics had to be changed to be consistent with this fact. This special theory of relativity predicted many unexpected physical consequences, all of which have since been observed in nature.

V

History of Light Theories

The earliest speculations about light were hindered by the lack of knowledge about how the eye works. The Greek philosophers from as early as Pythagoras, who lived during the 5th century bc, believed light issued forth from visible things, but most also thought vision, as distinct from light, proceeded outward from the eye. Plato gave a version of this theory in his dialogue Timaeus, written in the 3rd century bc, which greatly influenced later thought.

Some early ideas of the Greeks, however, were correct. The philosopher and statesman Empedocles believed that light travels with finite speed, and the philosopher and scientist Aristotle accurately explained the rainbow as a kind of reflection from raindrops. The Greek mathematician Euclid understood the law of reflection and the properties of mirrors. Early thinkers also observed and recorded the phenomenon of refraction, but they did not know its mathematical law. The mathematician and astronomer Ptolemy was the first person on record to collect experimental data on optics, but he too believed vision issued from the eye. His work was further developed by Egyptian scientist Ibn al Haythen, who worked in Iraq and Egypt and was known to Europeans as Alhazen. Through logic and experimentation, Alhazen finally discounted Plato’s theory that vision issued forth from the eye. In Europe, Alhazen was the most well known among a group of Islamic scholars who preserved and built upon the classical Greek tradition. His work influenced all later investigations on light.

A

Early Scientific Theories

The early modern scientists Galileo, Johannes Kepler of Germany, and René Descartes of France all made contributions to the understanding of light. Descartes discussed optics and reported the law of refraction in his famous Discours de la méthode (Discourse on Method), published in 1637. The Dutch astronomer and mathematician Willebrord Snell independently discovered the law of refraction in 1620, and the law is now named after him.

During the late 1600s, an important question emerged: Is light a swarm of particles or is it a wave in some pervasive medium through which ordinary matter freely moves? English physicist Sir Isaac Newton was a proponent of the particle theory, and Huygens developed the wave theory at about the same time. At the time it seemed that wave theories could not explain optical polarization because waves that scientists were familiar with moved parallel, not perpendicular, to the direction of wave travel. On the other hand, Newton had difficulty explaining the phenomenon of interference of light. His explanation forced a wavelike property on a particle description. Newton’s great prestige coupled with the difficulty of explaining polarization caused the scientific community to favor the particle theory, even after English physicist Thomas Young analyzed a new class of interference phenomena using the wave theory in 1803.

The wave theory was finally accepted after French physicist Augustin Fresnel supported Young’s ideas with mathematical calculations in 1815 and predicted surprising new effects. Irish mathematician Sir William Hamilton clarified the relationship between wave and particle viewpoints by developing a theory that unified optics and mechanics. Hamilton’s theory was important in the later development of quantum mechanics.

Between the time of Newton and Fresnel, scientists developed mathematical techniques to describe wave phenomena in fluids and solids. Fresnel and his successors were able to use these advances to create a theory of transverse waves that would account for the phenomenon of optical polarization. As a result, an entire wave theory of light existed in mathematical form before British physicist James Clerk Maxwell began his work on electromagnetism. In his theory of electromagnetism, Maxwell showed that electric and magnetic fields affect each other in such a way as to permit waves to travel through space. The equations he derived to describe these electromagnetic waves matched the equations scientists already knew to describe light. Maxwell’s equations, however, were more general in that they described electromagnetic phenomena other than light and they predicted waves throughout the electromagnetic spectrum. In addition, his theory gave the correct speed of light in terms of the properties of electricity and magnetism. When German physicist Gustav Hertz later detected electromagnetic waves at lower frequencies, which the theory predicted, the basic correctness of Maxwell’s theory was confirmed.

Maxwell’s work left unsolved a problem common to all wave theories of light. A wave is a continuous phenomenon, which means that when it travels, its electromagnetic field must move at each of the infinite number of points in every small part of space. When we add heat to any system to raise its temperature, the energy is shared equally among all the parts of the system that can move. When this idea is applied to light, with an infinite number of moving parts, it appears to require an infinite amount of heat to give all the parts equal energy. But thermal radiation, the process in which heated objects emit electromagnetic waves, occurs in nature with a finite amount of heat. Something that could account for this process was missing from Maxwell’s theory. In 1900 Max Planck provided the missing concept. He proposed the existence of a light quantum, a finite packet of energy that became known as the photon.

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