Electromagnetic Radiation (Light)

The second great area of physics necessary to address the universe is the subject of light, or electromagnetic radiationVisible light is the relatively narrow frequency band of electromagnetic waves to which our eyes are sensitive. Wavelengths are usually measured in units of nanometers (1 nm = 10 −9m) or in units of angstroms (1 Å = 10 −10m). The colors of the visible spectrum stretch from violet with the shortest wavelength to red with the longest wavelength.

However, electromagnetic radiation consists of more than just visible light; it also includes (from short wavelength to long wavelength) gamma‐radiation, X‐radiation, ultraviolet, visible, infrared (heat), microwaves, and radio waves (see Figure 1). All of these forms of light have both electrical and magnetic characteristics. The properties of light (see the section, “Particle properties of light”) allow us to build devices to observe the universe and to deduce the physical nature of the sources that emit the radiation received during these observations. However, these same properties mean that light interacts with other matter before it reaches the observer and this often complicates our ability to observe other objects in the universe. Note that the word “radiation” can refer to any phenomena that radiates (moves) outwards from a source, here electromagnetic or light radiation. The term should not be confused with radiation associated with a radioactive source, i.e. nuclear radiation.



Figure 1

The electromagnetic spectrum. Visible light is only a small portion of the electromagnetic radiation that can be detected by various instruments.

Particle properties of light

Light is such a complicated phenomena that no one model can be devised to explain its nature. Although light is generally thought of as acting like an electric wave oscillating in space accompanied by an oscillating magnetic wave, it can also act like a particle. A “particle” of light is called a photon, or a discrete packet of electromagnetic energy.

Most visible objects are seen by reflected light. There are a few natural sources of light, such as the Sun, stars, and a flame; other sources are man‐made, such as electrical lights. For an otherwise non‐luminous object to be visible, light from a source is reflected off the object into our eye. The property of reflection, that light can be reflected from appropriate surfaces, can most easily be understood in terms of a particle property, in the same sense that a ball bounces off a surface. A common example of reflection is mirrors, and in particular, telescope mirrors that use curved surfaces to redirect light received over a large area into a smaller area for detection and recording.

When reflection occurs in particle‐particle interactions (for example, colliding billiard balls), it's called scattering — light is scattered (reflected) off molecules and dust particles that have sizes comparable to the wavelengths of the radiation. As a consequence, light coming from an object seen behind dust is dimmer than it would be without the dust. This phenomena is termed extinction. Extinction can be seen in our own Sun when it becomes dimmer as its light passes through more of the dusty atmosphere as it sets. Similarly, stars seen from Earth seem fainter to the viewer than they would if there were no atmosphere. In addition, short wavelength blue light is preferentially scattered; thus objects look redder (astronomers refer to this as reddening); this occurs because the wavelength of blue light is very close to the size of the particles that cause the scattering. By analogy, consider ocean waves — a row boat whose length is close to the wavelength of the waves will bob up and down, whereas a long ocean liner will scarcely notice the waves. The Sun appears much redder at sunset. The light of stars also redden in passing through the atmosphere. You can see the scattered light by looking in directions away from the source of the light; hence the sky appears blue during the day.

Extinction and reddening of starlight are not caused by just the atmosphere. An exceedingly thin distribution of dust floats between the stars and affects the light that we receive as well. Astronomers must take into account the effect of dust on their observations to correctly describe the conditions of the objects that emit the light. Where interstellar dust is especially thick, no light passes through. Where dust clouds reflect starlight back in our direction, the observer may see blue interstellar wispiness like thin clouds surrounding some stars, or a nebula (to use the Latin word for cloud). A nebula formed by scattering of blue light is called a reflection nebulae.

Wave properties of light

Most properties of light related to astronomical use and effects have the same properties as waves. Using an analogy to water waves, any wave can be characterized by two related factors. The first is a wavelength (λ) the distance (in meters) between similar positions on successive cycles of the wave, for example the crest‐to‐crest distance. The second is a frequency (f) representing the number of cycles that move by a fixed point each second. The fundamental characteristic of a wave is that multiplication of its wavelength by its frequency results in the speed with which the wave moves forward. For electromagnetic radiation this is the speed of light, c = 3 × 10 8 m/sec = 300,000 km/sec. The mid‐range of visible light has a wavelength of λ = 5500 Å = 5.5 × 10 −7 m, corresponding to a frequency f of 5.5 × 10 14 cycles/sec.

When light passes from one medium to another (for example, from water to air; from air to glass to air; from warmer, less dense regions of air to cooler, denser regions and vice‐versa) its direction of travel changes, a property termed refraction. The result is a visual distortion, as when a stick or an arm appears to “bend” when put into water. Refraction allowed nature to produce the lens of the eye to concentrate light passing through all parts of the pupil to be projected upon the retina. Refraction allows people to construct lenses to change the path of light in a desired fashion, for instance, to produce glasses to correct deficiencies in eyesight. And astronomers can build refracting telescopes to collect light over large surface areas, bringing it to a common focus. Refraction in the non‐uniform atmosphere is responsible for mirages, atmospheric shimmering, and the twinkling of stars. Images of objects seen through the atmosphere are blurred, with the atmospheric blurring or astronomical “seeing” generally about one second of arc at good observatory sites. Refraction also means that positions of stars in the sky may change if the stars are observed close to the horizon.

Related to refraction is dispersion, the effect of producing colors when white light is refracted. Because the amount of refraction is wavelength dependent, the amount of bending of red light is different than the amount of bending of blue light; refracted white light is thus dispersed into its component colors, such as by the prisms used in the first spectrographs (instruments specifically designed to disperse light into its component colors). Dispersion of the light forms a spectrum, the pattern of intensity of light as a function of its wave length, from which one can gain information about the physical nature of the source of light. On the other hand, dispersion of light in the atmosphere makes stars undesirably appear as little spectra near the horizon. Dispersion is also responsible for chromatic aberration in telescopes — light of different colors is not brought to the same focal point. If red light is properly focused, the blue will not be focused but will form a blue halo around a red image. To minimize chromatic aberration it is necessary to construct more costly multiple‐element telescope lenses.

When two waves intersect and thus interact with each other, interference occurs. Using water waves as an analogy, two crests (high points on the waves) or two troughs (low points) at the same place constructively interfere, adding together to produce a higher crest and a lower trough. Where a crest of one wave, however, meets a trough of another wave, there is a mutual cancellation or destructive interference. Natural interference occurs in oil slicks, producing colored patterns as the constructive interference of one wavelength occurs where other wavelengths destructively interfere. Astronomers make use of interference as another means of dispersing white light into its component colors. A transmission grating consisting of many slits (like a picket fence, but numbering in the thousands per centimeter of distance across the grating) produces constructive interference of the various colors as a function of angle. A reflection grating using multiple reflecting surfaces can do the same thing with the advantage that all light can be used and most of light energy can be thrown into a specific constructive interference region. Because of this higher efficiency, all modern astronomical spectrographs use reflection gratings.

A number of specialized observing techniques result from application of these phenomena, of which the most important is radio interferometry. The digital radio signals from arrays of telescopes can be combined (using a computer) to produce high‐resolution (down to 10 −3 second of arc resolution) “pictures” of astronomical objects. This resolution is far better than that achievable by any optical telescope, and thus, radio astronomy has become a major component in modern astronomical observation.

Diffraction is the property of waves that makes them seem to bend around corners, which is most apparent with water waves. Light waves are also affected by diffraction, which causes shadow edges to not be perfectly sharp, but fuzzy. The edges of all objects viewed with waves (light or otherwise) are blurred by diffraction. For a point source of light, a telescope behaves as a circular opening through which light passes and therefore produces an intrinsic diffraction pattern that consists of a central disk and a series of fainter diffraction rings. The amount of blurring as measured by the width of this central diffraction disk depends inversely on the size of the instrument viewing the source of light. The pupil of the human eye, about an eighth of an inch in diameter, produces a blurring greater than one arc minute in angular size; in other words, the human eye cannot resolve features smaller than this. The Hubble Space Telescope, a 90‐inch diameter instrument orbiting Earth above the atmosphere, has a diffraction disk of only 0.1 second of arc in diameter, allowing the achievement of well‐resolved detail in distant celestial objects.

The physical cause of diffraction is the fact that light passing through one part of an opening will interfere with light passing through all other parts of the opening. This self‐interference involves both constructive interference and destructive interference to produce the diffraction pattern.

Kirchoff's three types of spectra

Both dispersive and interference properties of light are used to produce spectra from which information about the nature of the light‐emitting source can be gained. Over a century ago, the physicist Kirchoff recognized that three fundamental types of spectra (see Figure 2) are directly related to the circumstance that produces the light. These Kirchoff spectral types are comparable to Kepler's Laws in the sense that they are only a description of observable phenomena. Like Newton, who later was to mathematically explain the laws of Kepler, other researchers have since provided a sounder basis of theory to explain these readily observable spectral types.


Figure 2

Kirchhoff's three types of spectra. a) A continuous spectrum (blackbody spectrum) is radiation produced by warm, dense material; b) an emission line spectrum (bright line spectrum) is radiation created by a cloud of thin gas; and c) an absorption line spectrum (dark line spectrum) results from light passing through a cloud of thin gas.


Kirchoff's first type of spectrum is a continuous spectrum: Energy is emitted at all wavelengths by a luminous solid, liquid, or very dense gas — a very simple type of spectrum with a peak at some wavelength and little energy represented at short wavelengths and at long wavelengths of radiation. Incandescent lights, glowing coals in a fireplace, and the element of an electric heater are familiar examples of materials that produce a continuous spectrum. Because this type of spectrum is emitted by any warm, dense material, it is also called a thermal spectrum or thermal radiation. Other terms used to describe this type of spectrum are black body spectrum (since, for technical reasons, a perfect continuous spectrum is emitted by a material that is also a perfect absorber of radiation) and Planck radiation (the physicist Max Planck successfully devised a theory to describe such a spectrum). All these terminologies refer to the same pattern of emission from a warm dense material. In astronomy, warm interplanetary or interstellar dust produces a continuous spectrum. The spectra of stars are roughly approximated by a continuous spectrum.

Kirchoff's second type of spectrum is emission of radiation at a few discrete wavelengths by a tenuous (thin) gas, also known as an emission spectrum or a bright line spectrum. In other words, if an emission spectrum is observed, the source of the radiation must be a tenuous gas. The vapor in fluorescent tube lighting produces emission lines. Gaseous nebulae in the vicinity of hot stars also produce emission spectra.

Kirchoff's third type of spectrum refers not to the source of light, but to what might happen to light on its way to the observer: The effect of a thin gas on white light is that it removes energy at a few discrete wavelengths, known as an absorption spectrum or a dark line spectrum. The direct observational consequence is that if absorption lines are seen in the light coming from some celestial object, this light must have passed through a thin gas. Absorption lines are seen in the spectrum of sunlight. The overall continuous spectrum nature of the solar spectrum implies that the radiation is produced in a dense region in the Sun, then the light passes through a thinner gaseous region (the outer atmosphere of the Sun) on its way to Earth. Sunlight reflected from other planets shows additional absorption lines that must be produced in the atmospheres of those planets.

Wien's and Stefan-Boltzman's Laws for Continuous Radiation

Kirchoff's three types of spectra give astronomers only a general idea of the state of the material that emits or affects the light. Other aspects of the spectra allow more of a quantitative definition of physical factors. Wien's Law says that in a continuous spectrum, the wavelength at which maximum energy is emitted is inversely proportional to temperature; that is, λ max = constant / T = 2.898 × 10‐3 K m / T where the temperature is measured in degrees Kelvin. Some examples of this are:

The Stefan‐Boltzman Law (sometimes called Stefan's Law) states that the total energy emitted at all wavelengths per second per unit surface area is proportional to the fourth power of temperature, or energy per second per square meter = σ T 4 = 5.67 × 10 8 watts/(m 2 K 4) T 4 (see Figure 3).


Figure 3

A graphical representation of continuous spectra for light sources of different temperature. Wien's Law is shown by the peak of radiation at shorter wavelengths for higher temperatures. The Stefan‐Boltzman Law is shown by the larger areas under each curve (representing the total energy emission at all wavelengths) for higher temperatures.


This simple principle produces a relationship between the total energy emitted by an object each second, the luminosity L, the radius r of a celestial object, assumed spherical, and the object's surface temperature. The total energy emitted per second = surface area × energy per second emitted by each unit area, or algebraically,

 

Quantitative Analysis of Spectra

The development of the theory of quantum mechanics led to an understanding of the relationship between matter and its emission or absorption of radiation. If atoms are far enough apart that they do not affect each other, then each chemical element can emit or absorb light only at specific wavelengths. The energies of photons at these wavelengths correspond to the differences between the permitted energies of the electrons of the atoms. The negatively charged electrons can be considered to be in “orbits” about the positively charged protons in the nucleus of the atom, each orbit corresponding to a different energy. Quantum orbits can only be at certain energy levels, unlike orbits governed by gravity which can be at any energy. Emission of a photon of light occurs when an electron “drops” from a high energy state to a lower energy state. Absorption occurs when a photon of the right energy permits an electron to “jump” to a higher energy state. Most importantly, the pattern of absorption or emission lines is unique to each element. The strength of emission or absorption depends on how many atoms of the particular element are present as well as the temperature of the material, thus permitting both temperature and the chemical composition of the material producing the spectrum to be determined.

If atoms are progressively jammed closer together, the wavelengths of emission or absorption by any given atom will be slightly changed, thus some atoms will emit/absorb at slightly longer wavelengths and others will emit/absorb at slightly shorter wavelengths. The majority of atoms will emit/absorb at the same wavelengths that they would if unaffected by neighboring atoms. Astronomers therefore can differentiate between circumstances where the emitting or absorbing atoms are thinly dispersed (the spectral features will look very sharp) and where they are tightly packed together (the spectral features are broadened). In the extreme case of high density, the emission lines become completely blurred together and one observes a continuous spectrum.

Doppler's Law

If a light source and observer are approaching each other, the observed wavelength of any spectral feature is shorter than what would be measured if the two were at rest with respect to each other. On the other hand, if the two are moving apart, the observed wavelength appears longer that the wavelength that would be measured at rest. The Doppler Shift or Doppler Effect is a recognition that the change of wavelength Øλ of a given spectral feature depends on the relative velocity of the source along the line of sight:

 

where Δ is the observed wavelength, Δ 0 is the rest or laboratory wavelength, v is the velocity toward (negative) or away (positive) from the observer, and c is the speed of light. Relative motion of a light source toward the observer results in a blueshift of the spectrum, as all wavelengths are measured shorter or bluer; relative motion of a light source away from the observer results in a redshift. This doesn't mean that the light literally turns blue or red, it means that the light has its color shifted toward the shorter or longer wavelength region of the spectrum, respectively (see Figure 4); in most situations the shift is very small because velocities are small compared to the speed of light. This simple form of the Doppler Law holds only if the velocity v is small with respect to the speed of light. A more complicated equation formulated by Einstein in his theory of relativity must be used if the source is moving near the speed of light.


Figure 4
The Doppler effect. The frequency of light waves appears to change, varying with the relative velocity of the source (S) and the observer. If the source and observer are drawing closer together, the observed frequency is higher that the emitted frequency, and the observer sees blueshift. If the source and observer are getting farther apart, the observer sees redshift.