Wave Propertiesof Light

In modern physics, light or electromagnetic radiation may be viewed in one of two complementary ways: as a wave in an abstract electromagnetic field, or as a stream of massless particles called photons. Although either is an acceptable description of light, for our purposes in introductory astronomy the wave description will be more useful.

Light as a Wave

The quantity that is "waving" is the electromagnetic field, an esoteric but quite measurable entity: your lights shine and your microwave runs and your radio plays because the electromagnetic field exists. As illustrated in the adjacent image, a wave has a wavelength associated with it.

It is normal to give the wavelength of light the symbol Greek "lambda". Some common units of length employed for wavelengths of electromagnetic radiation are summarized in the following table. (The micrometer is often still called by its old name, the micron.)

Units of Wavelength
Unit Symbol Length
centimeter cm 10-2 meters
Angstrom 10-8 centimeters
nanometer nm 10-9 meters
micrometer nm 10-6 meters

Wavelength, Energy, and Frequency

The speed of light in a vacuum is commonly given the symbol c. It is a universal constant that has the value
c = 3 x 1010 cm/second

The speed of light in a medium is generally less than this. Normally the term "speed of light", without further qualification, refers to the speed in a vacuum.

A wave can be characterized by its wavelength, but we can also characterize it by the frequency (how many wavelengths pass a fixed point in a given time; think of sitting on the dock---of the bay---counting the number of water waves passing in one minute) and the energy that it carries (think of a water wave knocking you over in heavy surf). For light waves the relationship among the wavelength (usually denoted by Greek "lambda"), the frequency (usually denoted by Greek "nu"), and the energy E are

where c is the speed of light and h is another universal constant called Planck's Constant that has the values
h = 4.135 x 10-15 eV-sec = 6.625 x 10-27 erg-sec

in two different useful sets of units (eV stands for "electron volts"; electron volts and ergs are two common units of energy). Thus, these equations allow us to freely inter-convert among frequency, wavelength, and energy for electromagnetic waves: specifying one also specifies the others.

Radio waves have wavelengths from a few millimeters (microwaves) to kilometers. The wavelength of visible light is short. Visible light ranges from about 4 x 10-7 to 7 x 10-7 meters or 400-700 nm. Often different astronomers from different fields use different units to describe the same phenomena. (Do not confuse the physical concepts with the choice of units.)

Light as a Particle

We have described the wave properties of light but Einstein won his Nobel prize NOT for relativity but for something called the photo-electric effect. This effect demonstrated that a light meter measures light in discrete bundles called PHOTONs. There are some contexts in which light behaves as a particle, and other contexts where it behaves as a wave. In fact Newton had the feeling that light was made up of particles but now we know that it exhibits both wave like and particle like characteristics. One can think of light as being composed of many photons or "bundles of waves" each wave with a particular frequency (or wavelength).

Thus another way to think of the above formula for the energy of electromagnetic radiation is to say that it describes the relation between a photon's energy and its wavelength.

Some Light Exercise

Here are some exercises illustrating the conversion among energy, wavelength, and frequency for electromagnetic waves.