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.

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.