General Astronomy/Properties of Light and other Electromagnetic Radiation

Light is a medium of energy through which we perceive and interact with our environment. It is the visible frequency range of electromagnetic radiation which also includes invisible forms of electromagnetic radiation such as ultraviolet, infrared, and radio waves.

Like all electromagnetic radiation, light is transmitted by individual packets (or quanta) of energy known as photons. These photons are the units by which the combined forces of electricity and magnetism are communicated between other particles, such as the electrons associated with an atom. Depending on the circumstances under which it is observed, a photon can behave like a particle or as a wave. This principle is known as wave-particle duality.

Wave properties

The wave-like nature of electromagnetic radiation means it can be plotted on a graph as an oscillating electric and magnetic field at right angles to the direction of travel of the wave. The frequency of these oscillations is measured in the number of complete cycles per second, or hertz. The particular frequency of a photon places it somewhere on a spectrum of possible frequencies. This is referred to as the electromagnetic spectrum. The range of frequencies that form the visual spectrum lies between 3.8×10¹⁴ hertz (dark red) and 7.5×10¹⁴ hertz (violet).

The speed of light, given the symbol c, has been precisely measured as 299,792,458 m/s or approximately three hundred thousand kilometers per second and has been demonstrated to be constant in a vacuum. A vacuum being defined for the purposes of theory and experimentation as a volume of space that is essentially empty of matter. The speed of light is a fundamental constant of modern physics and remains constant regardless of the movement of the observer. Thus, for example, if you were somehow able to travel at half the speed of light, and you measured how quickly light was arriving from the front, you would measure it as arriving at the speed of light (3.00 x 10⁸ m/s).

Since the speed of light is a constant in a vacuum, for a given frequency a photon will have a corresponding wavelength, or the distance between the crests of the wave. The frequency and wavelength of light are directly related by the following equation:

$c=f\cdot \lambda$

where c is the conventional symbol for the speed of light, usually in meters per second, f is the frequency of light in hertz, and λ is the wavelength in meters.

Given the speed of light as 3.00 × 10⁸ meters per second, then the wavelength range for the visual spectrum is about 400 to 800 nm, or nanometers. (A nanometer is 10⁻⁹ meters, or one-billionth of a meter.)

The shorter wavelength of 400 nm corresponds to the greater frequency, and is located at the blue end of the visual spectrum. Likewise the longer wavelength of 800 nm belongs to the red end of the spectrum. The actual energy of the photon increases with decreasing wavelength (or increasing frequency.)

Einstein won the Nobel Prize for applying Planck's theories to electromagnetism.

Intensity

The intensity of a source of radiation is the energy it emits per unit of surface area per unit of time and has the units of Joules/(meter² x second). As the energy radiated by a spherical surface, I₀, moves away from that surface the radiation intensity decreases as the inverse of the distance squared (I=I₀/d²) because the radiation spreads out. In other words, the perceived intensity of a light source by an observer is inversely proportional to the distance from the light source squared. Thus for each doubling of distance from the source, the intensity drops by a factor of four, or 2 × 2.

The brightness of stellar objects, such as a star, are determined by the amount of light they radiate and their distance from the Earth. A bright star in the sky might actually be much more distant than an a dimmer star, but because it is more intense and radiates a greater amount of light it appears to be closer.

Astronomers record the light intensity of a stellar object as a numerical magnitude. The magnitude is a number on a logarithm scale that has been standardized, so that 5 steps in magnitude is equal to a multiple of 100 in intensity. In addition, the value of the magnitude increases as the intensity of the light source decreases.

Thus a star of magnitude 2.0 is dimmer than a star of magnitude 1.0. A magnitude 1.0 star is also 100 times as bright as a magnitude 6.0 star. Each +1.0 magnitude increase is the same as dividing the intensity by 2.512.

The reference point for the magnitude scale is set to zero. At one time this was based on the star Vega, or α Lyrae. The brightest star Sirius (α Canis Majoris) has a magnitude of −1.46. The limiting magnitude for a typical person's unaided eye is considered to be 6.0. However people have observed stars fainter than this under good conditions. Much fainter stars can be seen by using the larger collection area of a telescope and the extended recording ability of a camera.

Reflection

A mirror is a flat or curved surface usually made out of a highly-conductive material, such as a metal. When light interacts with a mirrored surface, it undergoes specular reflection. That is, a beam of light striking the mirror is reflected in only one direction. This direction is determined by the law of reflection, which states that the angle with the surface at which the light is reflected is the same as the angle with the surface at which it approaches.

In this illustration, the reflected light rays reaching the eye from an object produce the illusionary appearance of a reversed-image object behind the mirror.

The movement of a photon with respect to the mirror consists of two components. The first is the proportion of the movement parallel to the mirror, and the second is the portion perpendicular to the mirror. After the reflection, the portion parallel to the mirror is unchanged. However the portion perpendicular is now in the opposite direction. That is, it effectively "bounces" off the surface almost as a rubber ball bounces off the ground.

When light interacts with a surface that is not reflective, a portion of the light is absorbed by the surface and the remainder is scattered in random directions. This type of reflection is called diffuse, and it is responsible for the illumination effect of ambient light.

The portion of light absorbed by a surface is termed its albedo. The lower the albedo rating, the less light it reflects in a diffuse manner. A surface with a low albedo rating appears dark to an observer, while a high albedo rating appears light. The albedo rating of a surface can tell an astronomer something about the nature of the surface. For example, a surface covered with carbon soot will have a low albedo, while an icy surface has a higher albedo.

Refraction

When light passes at an angle through a transparent medium, the material causes the photons to change direction slightly. This change in angle is called refraction, and the angle by which the light is bent is determined by the index of refraction of the material.

In this illustration, the indicent beam of light strikes a glass surface at an angle θ1. A portion of the light energy is refracted through the glass at angle θ2. Most of the remaining light energy is reflected at angle θ'1.

The index of refraction of the two materials that the light passes between can be used to determine the change in angle by means of Snell's law. For materials with indices of refraction n₁ and n₂, the angle in the first material θ₁ determines the angle in the new material θ₂ as follows:

$n_{1}\cdot \sin(\theta _{1})=n_{2}\cdot \sin(\theta _{2})\,$

Here are the indices of refraction (at a wavelength of 589 nm) for some common transparent materials relative to a vacuum:

Material	Index
Air	1.003
Water ice	1.331
Water	1.333
Quartz	1.46
Crown glass	1.52
Dense flint glass	1.66
Diamond	2.419

where the index of refraction for air is at sea level with a temperature at the freezing point of water, and the water is at 20 °C.

Spectrum

For a given transparent material, such as glass, the refraction of light varies with frequency. A white light consists of photons of various energies. The red photons in the light will be deflected at a different angle than the blue photons.

If the light passes through a transparent material with parallel sides, such as a sheet of glass, the beam will emerge at the same angle as it entered. However when the two sides are not parallel, the angle will vary depending on the frequency. This is the principle behind the prism. A glass prism is used to separate the photons from a light source into a spectrum of frequencies from red to blue. A similar principle is what creates a rainbow as the light from the sun passes through droplets of water.

The index of refraction varies by frequency, causing parallel, monochromatic light rays from the left to emerge from the prism at different angles.

An instrument specifically designed to display the spectrum of a radiating object, such as a star, is called a spectroscope.

The early spectroscopes were constructed using a series of prisms that would successively spread the spectrum further apart. The problem with this arrangement, however, is that each of the prisms would absorb some of the light passing through. This limited the brightness of the objects that could be observed. An instrument called a diffraction grating, which was a mirror with a series of ruled parallel grooves, used the principle of diffraction to produce a spectrum with only minor loss of intensity.

Isaac Newton discovered that a light beam can be diffracted only so far, and no farther. The diffraction can be recombined into white light.

Lens

The lens takes advantage of the property of refraction to bend the light from a distant object and to make it appear closer (or more distant). A lens is, in a simplified sense, a prism that has been "wrapped" around in a circle, so that the light is bent symmetrically.

Because light of different frequencies is bent at different angles, however, the point at which the light comes to a focus varies with frequency. An observer looking through a lens would see light sources near the edge have a rainbow-like appearance. This is called chromatic aberration.

To adjust for this variation in the focus by frequency, opticians typically use combinations of lenses made of different materials (with differing indices of refraction). Judicious use of materials and lens shapes will result in a lens that focuses all the light at the same distance, producing a good quality image that does not suffer from chromatic aberration.

Magnification

When you observe an object nearby, it subtends an certain angle within your sight. That is, if you had an imaginary line running from the top of the object and your eye and a similar line from the bottom of the object to your eye, there would be a certain angle between these lines.

As the object recedes into the distance, the angle it subtends across your sight steadily decreases until it becomes nearly a point. The imaginary lines from the top and bottom of the object are now nearly parallel. In fact, for an astronomical object such as a star, these lines are essentially parallel.

In order to enlarge the appearance of an object, it is necessary to modify the paths of the incoming light rays so that they are no longer parallel but instead arrive at an angle as they enter your eyes. The eye then perceives the object as if it were much closer.

There are two common means for causing the parallel light rays to converge in this manner. The first involves the use of a curved, concave mirror. The second takes advantage of the refraction ability of materials such as glass to redirect the light inward at an angle.

The shape of glass needed to accomplish this is a convex lens. The portions of the lens near the center need little curvature since they will are required to bend the light only slightly toward your eye. At the edges of the lens, however, the light needs to be bent at a sharper angle, so the sides of the lens become bent toward each other like a prism. Overall the sides of the lens form a smooth curve that gradually increases in slope toward its edges.

A well-made convex lens will cause the parallel light from a distant light source to focus at a point. When there are multiple such light sources, they are each focused at a point on a plane, known as the focal plane. The human eye can perceive the image of this plane, and the result is a magnification of the view. If the images do not focus on a plane, then the image will appear blurry.

Diffraction

Another wave-like property of light is a tendency to bend and spread whenever it meets an obstacle. Any beam of light will also tend to spread with distance, so that it becomes impossible to maintain a tight beam of an arbitrary length. The property of diffraction is what limits the resolution of a distant object.

When a beam of coherent light, such as that produced by a laser, is passed through two slit openings, the light radiates from the slits like ripples in a pond. The semi-circular ripples from the two slits interact with each other, sometimes adding together their wave heights and at other times cancelling each other out. This is called constructive and destructive interference. If a screen is placed in the area where these ripples interact, alternating bands of light and darkness would appear.

Resolution

The resolution of a viewing instrument is a measurement of how well it can be used to distinguish two points that are very close together. For example, the two points could be the two stars in a binary star system. In astronomy, resolution is usually measured in seconds of arc. The resolution can vary depending on a number of environmental and quality conditions, but it is always limited by the aperture of the observing instrument. That is, there is a best possible resolution that any particular telescope can achieve. To get better resolution, a larger aperture is needed.

To see why this is so, imagine a telescope that consists of only two vertical slits separated by some distance, with a viewing screen behind. When the light from a distance star enters this telescope, it passes through the slits and forms an interference pattern on the screen. The distance between the light and dark bands is proportional to the wavelength of the light and inversely proportional to the distance between the slits. Thus increasing the separation of the slits will reduce the width of each band.

Now suppose there are two stars. They will both form bands of light and dark light on the screen, which may overlap. The closer the two stars are two each other, the closer their interference bands approach until they become indistinguishable. But if the separation of the slits is increased, then the bands become narrower and the stars can be distinguished again. This is the principle behind the interferometer.

Interferometer

In an ordinary telescope, the resolution is determined by the aperture. In this respect, a telescope can be thought of as a whole series of slits allowing light through, with the light at the outer edge providing the maximum resolution. The resolution of the telescope can be improved by adding a set of mirrors outside the maximum aperture that collect peripheral light rays, and effectively increase the aperture.

Similarly, two or more telescopes can be configured to work together and provide an aperture at least equal to the separation of their collecting surfaces. This setup is called an interferometer, because the images from both telescopes are integrated through a process of diffraction interference. Radio telescopes have successfully used this technique for many years to achieve very high levels of resolution. Optical interferometers are more difficult to build due to the requirements for extreme precision and the need to dampen out any vibrations.

Reflection gratings

Reflection gratings are surfaces that have been very precisely ruled with a series of parallel grooves. The grooves have a saw-tooth pattern, with each groove consisting of a long flat surface machined at a slight angle, with a sharp step at the edge. Each of the grooves is very narrow, with about 600 lines per mm (15,000 per inch).

As light is reflected from each of the grooves, it is slightly behind the light from the adjacent grooves. This difference produces an interference effect that reinforces the light at certain angles and cancels out the light at others. The grating is very efficient at destructively interfering with the light except at one particular angle, where the light constructively interferes and produces a peak intensity. The angle of this peak varies by the wavelength of the light, so a spectrum is produced.

Polarization

In addition to a direction of travel, a photon is composed of an electric and magnetic field. These lie at right angles to each other and to the direction of travel. This is known as a transverse wave. These perpendicular fields give the photon an orientation. The fields of each photon will maintain their orientation while traveling in a vacuum. Fields of this type are called plane-polarized.

Normally light from a source consists of a large number of photons that have a random polarization. However, it is possible for a number of the photons to become oriented in the same direction, becoming polarized. This coherent orientation can be detected by means of a sheet of polarizing material. When the sheet is oriented in the direction of the polarization, the polarized light passes through. As the sheet is rotated, it transmits a decreasing portion of the polarized light until finally, at right angles to the plane of polarization, it blocks all of the polarized light.

Light can become partly polarized by reflecting from a surface, such as sunlight reflecting off a pool of water. Reflected sunlight provides a source of glare for somebody driving a vehicle. Because this light is partially polarized, the use of polarized sunglasses helps reduce glare by blocking the polarized light preferentially.

Astronomers can examine a stellar light source to determine whether it is a source of polarized light. The presence of polarization is an indication of certain physical properties in effect at the source of the light, or along the line of sight of the light rays. For example, a magnetic field can polarize a light source, as can the acceleration of an electron to a velocity near the speed of light.

Spectral lines

When an atom absorbs a photon of light, the energy is forces the absorbing electron in the atom into an excited state. The electron changes its behavior, effectively becoming more energized and entering a new orbital pattern about the nucleus. A sufficiently energetic photon, or a combination of photons with enough energy, can even knock the electron from the atom. The atom then becomes ionized and gains a net positive charge.

Due to the quantum nature of small particles, the changes in energy allowed for an electron in an atom is fixed to very specific amounts. When a photon of just this energy is captured by the electron, it is must jump to a new and higher energy level. Thus each atom has a specific set of energy bands where it will favorably absorb photons, depending on the current energy states of its electrons.

When a white light is passed through a gas composed of the same type of atom, those atoms will tend to absorb light at those frequencies that match the energies needed for their electrons to jump to a new level. An observer on the other side of the gas who looks at the spectrum will see dark lines where these energies have been absorbed. Likewise an observer looking at the gas from another angle will see bands of light where those same energy frequencies were emitted by the atoms.

This property of selective absorption of light at specific bands is important in astronomy because it allows an astronomer to determine the chemical properties of a distant object. A star, for example, will radiate a spectrum with strong or weak absorption bands, which are determined by the quantities of different gases on its surface. The science of recording and measuring these lines is called spectroscopy.

Doppler shift

As an object moves toward us in space, it may radiate light in our direction. The velocity of the light we receive does not change. However, during the time interval between each of the peaks in the light wave it is transmitting, the object has moved slightly closer toward us. Thus the wavelength grows shorter and appears more blue than normal. Correspondingly, an object moving away from us will have its wavelength stretched out, making it appear more red.

This red-shift or blue-shift property has a number of important applications in astronomy. It can be used to measure the velocity with which a distant object, such as a galaxy, is moving toward or away from us. For objects that are rotating, we can measure the rate of rotation by comparing the blue shift on the edge rotating toward us to the red shift of the edge moving away. We have also discovered binary stars by the regular oscillation of the spectrum toward the blue or the red as the star orbits its companion.

Spectrometry and Photometry

Spectrometry involves looking at the spectra of light. Spectra are what you get when you take light from a source and spread out the colors by passing the light through a prism or over a grating, and then looking at the amount of light at a certain wavelength. There is a huge amount of information that you can get from doing this.

So let's take a spectroscope and point it at something like a fluorescent light bulb or a nebula. The thing that you will see is that rather than a continuous rainbow of all colors or wavelengths, the light is actually a combination of light from different well defined wavelengths. You will see lines.

The reason for these lines is that the electrons in the gas in the fluorescent lights can only be at certain energy levels. When you do something to energize the gas in a fluorescent bulb, the electrons in the atom's gas move to higher energy orbits, which are known as excited states. They stay in those excited states for a length of time ranging from milliseconds to seconds. When the electrons drop from the high energy states to lower energy states, then they will emit light at a wavelength that has an energy (and a corresponding wavelength) equal to the difference between the two energy states. This is known as an emission spectrum.

The detected spectra gives insight into the composition of the object emitting the spectra. Every element and material has its unique set of energy levels and unique lines, and by comparing those the lines of emission spectra with those of known elements, it's possible to discover the object's composition.

When you add energy to an atom, the electrons move to a higher energy state. As the electron relaxes and moves down the energy states, it emits a particle of light for each transition that it makes. Since every energy has a particular color associated with it, each transition puts out light at a single wavelength. The time between stimulation and re-emission is very rapid (in like a microsecond), but there are some materials in which the transition from a high energy state to a low energy state takes a long time. An example of this is glow in the dark stickers. When you expose it to light, it kicks some of the electrons into high energy levels, and it takes seconds to minutes for the electrons to revert to their original state.

One can discover other things about an object from its spectrum. For example, as you increase the temperature, you end up with more and more electrons in higher energy states and this affects the spectrum in that you end up with stronger lines. But if you increase the temperature past a certain point, the electrons leaves the atom completely and the lines become weaker.

You can also discover the pressure and density of the object. As the pressure and density increase, there is a increased chance that particle interactions will change the electrons' energy states to higher or lower level. This causes the lines to grow wider since there is a higher chance that the electron won't start and finish at a particular energy level.

If you increase the pressure and density enough the electrons no longer have enough time to stay at a certain energy level, and so the lines broaden to form what is known as a continuous spectrum, A continuous spectrum is emitted by a solid, liquid, or high pressure gas. Because the electron is no longer restricted to certain energy levels and certain wavelengths, the electron will often emit a low energy infrared photon rather than a photon of light. As a result something that is emitting a continuous spectrum (like a light bulb, specifically an incandescent light bulb) will emit much of its energy at lower frequencies (called heat) compared to something that is emitting a more discrete spectrum (like a fluorescent light bulb). Since energy is conserved, a fluorescent light bulb emits almost all its energy at a few wavelengths very efficiently while an incandescent light bulb emits much of its energy as heat. Hence, a florescent bulb will convert electrical energy into light more efficiently.

There is one more type of spectrum which is very common. If you expose a gas to light of different wavelengths and one of those wavelengths happens to match a difference in energy levels in the gas, it will absorb the light at that particular wavelength. So, if you have a source of a continuous spectrum pass it into cool gas in front of it, you produce what is known as an absorption spectrum. Most stars emit absorption spectrum as the cool upper layers of the stars absorb lines from the light emitted by the hot lower levels of the star.

So far we have been talking just about visible light, but the principles of spectroscopy apply to other types of electromagnetic radiation, of which visible light is just a small slice in the overall range of wavelengths. You can have gamma ray or X ray spectra (at shorter wavelengths than visible light) as well as microwave and infrared spectra (at longer wavelengths than visible light). The big difference has to do with what generates the radiation. The energy differences between different states of an atom typically are the energy of a particle of visible light. An X-ray photon will knock the electron right out of an atom, as a result an X-ray can't be generated by electrons transitioning between atomic energy levels. However, X-rays are generated when atomic nuclei transition between different nuclear energy levels. Conversely, microwave radiation can be generated when molecules move between energy states as they "wiggle." So by observing microwaves you can detect cool clouds of molecular gas by detecting microwaves in the spectrum. Conversely by sending microwaves into something that contains water the molecules will be induced to "wiggle" or in other words heat up. At the same time, the microwaves will pass through things (air or ceramic) whose energy levels don't match the microwaves. So if you put something like a cup of coffee in a microwave oven, all of the energy will be absorbed by the coffee and not by the cup or the air.

One final thing about spectroscopy. Spectrographs are affected by so many things and that every object out there has a different spectrum, and understanding what affects spectrographs and how to glean this information from spectrographs is an important part of astronomy.

Discussion questions

• The stellar classification system from hottest to coolest is OBAFGKM with A being the star with the strongest hydrogen line, B being next strongest and so forth. Why is the stellar classification in this order rather than the more logical order of temperature? Discuss a case from your experience in which a similar reason has led to seemingly odd classification systems.

• Identify three objects and tell me whether they would result in an emission, continuous, or absorption spectrum. Also tell me what you would see if you pointed a spectroscope at you. Would you see an emission, continuous, or absorption spectrum?

• What type of spectrum do you suppose an LCD puts out? What about gold? What about a microwave oven? What about you?

• Using your knowledge of advances in photography, how do you suppose an astronomer takes a spectrum differently today than in 1920? What about 1850? How do you think the Internet can be used to help astronomers take spectra?

• Why do you think it is so tough to create a good looking fluorescent light bulb and how do you think that they do it.

• If I stand in front of 100 watts of radio waves or light waves, nothing bad happens to me. But if I stand in front of 100 watts of gamma rays or X-rays, bad things will happen to me. Why?