EMR spectrum, optical and radio "windows"
EMR spectrum, more detailed infrared transmission.
These 3 diagrams show the electromagnetic spectrum and the wavelength bands over which the Earth's atmosphere allows radiation to pass (primarily in the "visual window" and "radio window"). The visual window wavelength range can also be called the "visible window" or the "optical window". Of course our eyes sense the different wavelengths over the visual range as different colors, as shown in the color bar. The wavengths in the color bar are given in nanometers (nm). 1 nm= 1 billionth of a meter. Note that red light has the longest wavelength in the visible range and violet the shortest wavelength in the visible range, but other forms of EMR have wavelengths far longer than red light and far shorter than violet light. Hence the names "infrared" (infra- mean "beneath" or "below"), or light below red (in frequency) and "ultraviolet" (ultra- means "beyond" or "above"), light above violet in frequency.
The first graph (TA36) shows the frequency (in Hz = Hertz, or cycles per second) on top and the wavelengths (in meters) on bottom. Note that the numbers on top get larger as you move to the right, while the numbers on the bottom get smaller as you go to the right (the arrow on the bottom is somewhat confusing- it does NOT point in the direction of bigger numbers but of smaller numbers "Decreasing wavelength").
The different graphs give somewhat different regions called "radio waves", "infrared" etc. There are no sharp divisions between these different forms of EMR- they only differ in wavelength and frequency from each other, so the distinctions between, say, radio and microwaves is somewhat arbitrary.
The inverse square law. As light (or any EMR) travels away from its source, it spreads out to cover a larger and larger area. Thus, the flux, or amount of light per unit area, drops with distance. The flux goes as the inverse of the square of the distance- for example if we have two light sources with the same power or luminosity, but one is 3 times as far from us as the other, the flux we measure from the more distant one will be 1/9 that of the closer light source.
The flux is what we see as brightness- a bright star has a high flux, while a faint star has a low flux.
Luminosity, flux and distance Just another way of looking at the inverse square law. The luminosity of a source of EMR is the total power emitted. This is measured in units of Watts (W). At a distance d from the source, an observer measures a flux (f) of power from the source. Flux has units of watts per square meter (W m ^-2). If the source emits isotropically (equally in all directions) and there is no absorption of photons between source and observer then the same amount of power (equal to the luminosity) must pass any sphere at any distance (assuming the EMR has had time to get to the distance d).
In astronomy we measure f (using a telescope and detector- usually over only a limited wavelength range), try to get d (from various techniques, depending on the type and distance of object we are studying), then calculate L.
Apparent magnitudes Astronomers usually talk about the flux of a star in terms of its apparent magnitude. This idea goes way back to Hipparchus, a Greek astronomer who lived more than 2100 years ago. The scale appear to go "backwards"- bigger number mean smaller flux (fainter stars). The scale is also a ratio scale- a change of 5 magnitudes corresponds to a change in flux of a factor of 100.
The flux of objects shown on the graph covers an enourmous range- from the Sun to the faintest objects we can see with the largest telescope spans a range of about 50 magnitudes. Each 5 magntudes is a FACTOR of 100 in flux, so a difference of 50 magnitudes corresponds to a factor in flux or brightness of 100x100x...x100 (100 multiplied by itself 10 times)= 100 million trillion!
Continuous spectra of blackbodies of various temperatures Every solid or dense gaseous body radiates a continuous spectrum called a blackbody spectrum. The word "blackbody" is quite confusing- the Sun radiates a blackbody spectrum, but it sure isn't black! The wavelength of the peak of the emission depends on the surface temperature of the body. The hotter the body, the shorter the wavelength of the peak emission. The Sun, with a surface temperature of about 5700 Kelvin, radiates mostly visible light (visible EMR). A hotter star (an example of a 50000 Kelvin star is shown) would radiate mostly ultraviolet EMR. You and I, with a body temperature of 98.6 Farenheit (or 310 Kelvin) radiate or emit infrared EMR. Of course, our eyes are not sensitive to infrared EMR, which is why you can't see yourself glowing if you are in a dark room (one with no sources of visible EMR). In your normal everyday life, you see people and objects near room temperature only by visible light that is REFLECTED by the body- not EMITTED by the body. The visible light is usually from a hot body (Sun or lightbulb filament, but there are also "cool" things that emit visible light- such as LEDS - but these do not emit blackbody radiation, but a form of emission line spectrum).
Spectrum of the filament in an ordinary incandescaent light bulb.. An ordinary (incandescent) light bulb produces light when a metal filament (made of the metal tungsten) is heated to about 2300 degrees Kelvin by passing an electric current though the filamant. The filament gives off blackbody radiation, with the maximum emission at a wavelength (lamda- max) of about 1250 nm. As seen in the graph, only a small fraction of the light's EMR is in the visible region of the spectrum, from about 400 to 700 nm, where our eyes are sensitive. Thus, most of the electrical energy is wasted, as it produces infrared radiation which can not be detected by the human eye. The infrared radiation is absorbed by the bulbs surroundings and turned into heat, which may be fine in the winter, but in the summer this wasted energy is doubly bad- you have to pay more for your airconditioning bill to get rid of the useless heat generated by the filament. If we could run the filament at a higher temperature, then the bulb would make a higher fraction of useful light, but then the filament would melt.
Light bulb and Wien's Law Here is a practical application of Wien's Law. The spectra show the spectral energy vs. wavelength for an ordinary incandescent light bulb. Note that the peak is in the infrared, and only a very small fraction of the emitted EMR is useful light that our eyes can see. (Much of the EMR is *worse* than useless- in a building, the IR energy heats up the building and often one must pay more in A/C bills to remove the heat!) Why? Application of Wien's law shows that the filament temperature is 2320 K. To get more useful light, the filament would have to be made to run hotter. This is possible, but then the filament would rather quickly evaporate.
Spectral energy distribution of Sun The spectral energy of the Sun can be fitted with a 5800 K blackbody curve over a wide range of wavelengths, particularly in the visible and infrared where most of the Sun's energy is emitted. The Sun has much more x-ray emission than can be accounted for by a 5800 K source. These x-rays come from the hot corona, a very hot (2E6 K) but very optically thin gas surrounding the optically thick photosphere of the Sun.
