Saturday, January 23, 2010

This post is part of a primer on infrared spectroscopy and global warming. The  main post gives an overview of the topic and provides links to each of  the sections. This post examines what infrared radiation (IR) is, a necessary first step to understanding the importance of IR in discussions about global warming.

Figure source

IR is a type of electromagnetic radiation; so the starting place is to understand electromagnetic radiation.

Electromagnetic radiation is all around us and is part of our daily lives.  Visible light is perhaps the most familiar type of electromagnetic radiation.  Radio, microwave, infrared, and ultraviolet radiation are also familiar.  All of these types of radiation are examples of electromagnetic radiation.  They differ by what part of the electromagnetic spectrum they occupy.

Electromagnetic radiation can be treated as waves.  There are many types of waves, but here I focus on sinusoidal waves, which come in two basic flavors.  A wave that travels down a guitar string has a displacement from equilibrium that is perpendicular to the direction of travel.  A sound wave, on the other hand, is a compression wave  in which  the displacement from equilibrium is along the direction of travel.  The first type of wave is a transverse wave.  the second type is a longitudinal wave.  Electromagnetic radiation is a transverse wave; the displacement from equilibrium is perpendicular to the direction of travel.

Measures and Units of Electromagnetic Radiation

The distance between peaks in a wave is called the wavelength.  It is a unit of distance and can be measured in meters (m).  Appropriate prefixes are used depending on the order of magnitude of the wavelength.  For example, visible light is typically measured in nanometers (nm), whereas IR is typically measured in micrometers (μm) also known as microns. The symbol for wavelength is lambda, λ.

The number of cycles of the wave that occur per unit of time is called the frequency. The units for frequency are cycles per second. As "cycles" is not a real unit, frequency can be thought of as inverse seconds and is designated Hertz (Hz). 1 Hz = 1/s. So, for example, a frequency of one million cycles per second would be 1 megahertz (MHz). A way to think about this unit is to imagine that one is counting the number of wave peaks that pass by in a second. The symbol for frequency is ν.

If one multiplies the wavelength times the frequency, one gets meters per second, i.e., distance divided by time, which is a speed. In vacuum, this speed is the speed of light, denoted by c.

λν = c

The speed of light in vacuum is a constant. In air or other media, there is a correction factor. In air this factor is small and I neglect it here. Where it is relevant to the discussion, it will be revisited.

Notice that the equation can be rewritten as:

ν = c/λ

This equation means that the wavelength is inversely proportional to the frequency. So waves that have a large frequency have a small wavelength. For example, the frequency of blue light is is larger than red light; therefore red light has a longer wavelength than blue light. Infrared radiation has a lower frequency than visible light and therefore a longer wavelength.

If light is a wave, what is waving?

Acoustic waves are caused by longitudinal compression of the air or other media through which the sound is flowing.  Ocean waves are displacements of the water from its equilibrium position.  A wave in a guitar string is a displacement of the string from its equilibrium position.

Electromagnetic waves are displacements of the electric field and the magnetic field from their  equilibrium values.  This answer is not very satisfying because unlike water, air, or a guitar string, electric and magnetic fields are pretty abstract.  Nevertheless, to keep this primer on a basic level, I am not going to go into much depth on that topic.

As the name implies electromagnetic waves have an electric component and a magnetic component.  In its interaction with matter, the electric component is much more significant and for the most part, I will neglect the magnetic component.  A less obvious approximation that I am making has to do with the electric component itself.  I am going to treat electromagnetic radiation as electric dipole radiation.

Imagine a positive and a negative charge separated by some distance.  Imagine that the distance oscillates as a function of time.  The electric field generated by these charges is electric dipole radiation.  When electromagnetic radiation interacts with matter, this electric dipole component is the most significant interaction.  There are other interactions, but I will only delve into them in discussions where they are relevant.

The Infrared Spectrum

The infrared spectrum ranges from about 750 nm (0.75 μm ) to about 300 μm.  The wavelengths are longer than visible light.  As indicated above longer wavelengths mean lower frequencies; so the frequency of infrared radiation is lower than visible light.  The units that are commonly used for frequency in the infrared range may seem somewhat strange.  Common usage is to refer to the frequency of IR in inverse centimeters or wavenumbers (cm-1).  Recall that frequency is inversely proportional to wavelength:

ν = c/λ

It stands to reason that 1/λ is proportional to the frequency (again I neglect the vacuum correction).  The infrared spectrum lies between about 33 and 13,000  cm-1.

IR is invisible.  In the popular imagination, IR is often considered to be heat.  The reason for this idea is that room temperature objects typically absorb and emit IR.  Night vision technology uses the infrared region because objects can be seen in the infrared even when no visible light is present.  Hot objects are brighter in the infrared than cooler objects and the wavelength range is different.  This idea is discussed more in the post on on black-body radiation.

Energy, Quantization, Photons, and Planck's Constant

Although electromagnetic radiation (and therefore IR) can be treated as a wave, it can also be treated as a particle.  The reason for doing so is that the energy  is quantized.  There is a smallest amount of electromagnetic radiant energy that can be absorbed or emitted for a given wavelength.

Consider baseballs and butter as examples of quantized and continuous substances.  Baseballs are quantized; they are countable.  It makes sense to say that Bobby bought twelve baseballs.  It does not make sense to say that Bobby bought twelve butter.  Butter is a continuous quantity.   Sticks of butter are quantized, but butter itself is not.

It turns out that in some respects electromagnetic radiation is more like baseballs than like butter.  A single "particle" of light is called a photon.  It is not possible to absorb half of a photon, or 17.877 photons.  Photons are integral.  It turns out that the energy of a photon is proportional  to the frequency:

E = h ν

The constant of proportionality is called Planck's constant.  The implication is that photons of higher frequency have higher energy.    A gamma ray photon has more energy than an X-ray photon.  An X-ray photon has more energy than a UV photon, which has more energy than a visible photon.  Blue light has a higher frequency than red light; therefore, a blue photon has more energy than a red photon.

Infrared photons have more energy than microwave photons but less energy than visible light. The units of wavenumbers (cm-1 ) are sometimes treated directly as units of energy.

It makes sense that hotter objects emit more radiation than cooler objects, but it is also the case that hotter objects emit higher frequency radiation.  This fact should now make sense.  It is more "expensive" to emit a higher energy photon than a lower energy photon.  Objects that are rich in energy (hot objects) can "afford" to emit more high frequency photons.  Room temperature objects emit in the infrared, but if they are heated enough, they will eventually emit red light and become red hot.  As objects get even hotter, more visible frequencies become available.  Very hot objects emit throughout the visible spectrum and are perceived as white.  This same phenomenon occurs within the infrared spectrum, except that we cannot see it.  Warmer objects emit higher frequency IR photons than cooler ones.  This idea is expanded further in the next post in this series,  Infrared Radiation, Black-Bodies, and temperature.

Sources

Griffiths, David J., Introduction to Electrodynamics, 2nd edition, Prentice Hall, Englewood Cliffs, NJ, 1989

Hecht, Eugene, Optics, 4th edition, Addison Wesley, San Francisco, CA, 2002