How Do Spectrographs Work?

Snell?s law describes the angle at which it refracts, as a function of the index of refraction of the two different media:

 

n₁ sin θ_i = n₂ sin θ_r

 

We saw that n = c / v. But the speed of light is in units of distance / time and so is equal to λ / T, or wavelength / period. Thus:

 

n = cT / λ? =>

 

cT₁ / λ ₁ * sin θ_i = cT₂ / λ ₂ * sin θ_r

 

 

Now this is an interesting result: because the index of refraction is dependent on frequency (inversely proportional to wavelength), light of different frequencies or colors diffracts through different angles. That, then, is why the prism disperses light into its constituent colors.

 

My favorite dispersion device to use with my spectrographs is not, however, a prism: it is a diffraction grating. Click here for a description of the double-slit experiment (how gratings work). Basically a diffraction grating is a piece of glass or aluminum or some other material with lines engraved on its surface. It is more linear than a prism and usually preferred over prisms.

 

One might suppose that since a ruled piece of glass is all that is neccesary to disperse light into its constituent wavelengths, spectrographs are relatively easy to build. But building a spectrograph is not as simple as it might first seem. It is important that light rays hitting the grating (or the prism) be parallel to one another (collimated): This usually means that a lens is neccesary. A second lens is neccesary (in most, but not all cases) to focus the spectrum onto the camera.

 

 

One more component is (usually) essential for the success of a spectrograph, and that is a slit. The slit?which can be something as simple as a piece of cardboard with a thin slot in the middle, or more elaborate?is placed at the focal point.

 

So the components of a simple spectrograph are:

 

1. Slit
2. Collimation lens
3. Diffraction grating (or prism, grism, etc.)
4. Camera lens
5. Camera chip

 

There are other important considerations?the slit, for instance, must be exactly at the focal point of the collimation lens or it will not be sharply defined through the entire spectrum, and the grating must be just at the correct angle. Also, you can probably tell that in the diagram above there is a lens not drawn?the lens on the other side of the slit from the collimation lens. In astronomical spectroscopy this lens might be a telescope (in which case the entire spectrograph is attached to the back of the telescope) or in other types of spectroscopy (like Raman) it might be something like a microscope objective.

 

 

What do the lines mean?

 

You can graph intensity versus wavelength in a spectrum; this gives you a clearer picture of what you are seeing. Usually the word ?spectrum? has a connotation of this graph, and not just the strip image obtained by the camera.

 

Below I have a spectrum of the sun in a different part of the spectrum?the violet, blue, and part of the green.

 

 

In this spectrum I have labeled what are called the Fraunhofer lines. Fraunhofer was the German physicist who noticed the dark lines in the spectrum of the sun and, in the 19^th century, was the first to carefully study them. The lines appear as sharp dips in the graph shown above. At the time of his discovery, the significance of the lines, and the way they would completely transform the field of astronomy and other sciences, was still not known.

 

Later, other scientists, including Kirchoff?another German physicist?were experimenting with spectra of elements on earth. Just as you can obtain spectra of the sun, you can obtain spectra of more ordinary objects by heating them or shining light through them. It was realized that specific elements, when heated, had spectra of a rather special nature: their spectra had patterns of bright lines. The spectrum of each element was unique.

 

Here is a spectrum I took of a mercury lamp:

 

 

This spectrum, in the green and the yellow, is almost entirely dark except for three sharp, distinct emission lines. No other element has a spectrum like this: this means that if you see these lines in a spectrum you?ve taken, you know there?s mercury involved.

 

I see these lines a lot in astronomical spectra because flourescent mercury lamps are a common component of light pollution, and I see them in my Raman spectra (of chemicals) because of the screen on my laptop. J I generally use my mercury lamp to calibrate my spectra? But I digress.

 

Kirchoff noticed these lines in the spectra of elements. He noticed that some of the elemental lines (most noticably, hydrogen?s lines) corresponded to the dark lines in the sun. He realized the significance of this: suddenly there was a way to study the composition of the sun from the earth. The lines correspond to different elements (and molecules) in the sun?s atmosphere.

 

 

What does intensity of the spectrum at different wavelengths tell us?

 

We know that lines in the spectrum correspond to different elements. What, though, does the intensity of each line tell us? Why, in the spectrum of the sun above, were the lines dark?dips in the spectrum?and bright?sharp rises in intensity in the spectrum?in the graph above?

 

Stars are blackbody radiators, which means that, to a certain degree, they emit light at all wavelengths. A graph of the spectrum of an approximately blackbody radiator?which could be your kitchen stove as well as a star?is a specially shaped curve called a Planck curve. The shape of this curve depends on temperature. Hotter objects tend to be bluer; colder objects tend to be more red. So the peak of a cool star is at a lower wavelength than the peak of a hot star (in terms of wavelength, red << blue). This is important: it means that you can tell the temperature of the star by the shape of its spectral curve, after allowing for effects due to instrumental response and the earth?s atmosphere. And if you know the temperature of the star, you are closer to determining its absolute magnitude?how bright the star really is, independent of the distance from it to the earth. By knowing a star?s absolute magnitude and relative magnitude you can actually calculate its distance from the earth.

 

Blackbody curves are why the spectrum of the sun above was a rainbow: the sun is so hot that it emits light at many colors. The solar spectrum peaks at around 500 nm, which corresponds to green light. This peak also corresponds to a temperature of about 5770 K (http://www.lowell.edu/users/jch/workshop/gjr/gjr-p1.html). There is an interesting consequence of this: because the sun peaks in green light, human (and other animal) eyes are most sensitive to green.

 

The dark lines are because of elements in the atmosphere of the sun. In passing through the atmosphere, some light from the sun?s hot core is absorbed. Integral to the understanding of spectroscopy is the concept that only light of discrete wavelengths is absorbed?only photons of sufficient energy to knock electrons in elements to the next shell, in other words. Mercury would cause dark lines in the sun spectrum at the exact same wavelengths that it caused bright lines in the spectrum I took shown above.

 

There are many other things that you can tell from astronomical spectroscopy: you can tell the speed of gases in the star because of an effect called Doppler broadening, and you can compare relative abundances of elements by comparing intensities of different lines in stellar spectra.

 

And, of course, spectroscopy is not just astronomical. Raman spectroscopy is my favorite type of non-astronomical spectroscopy: it deals with the spectra of molecules. Essentially, spectroscopy on earth is just the same as astronomical spectroscopy: it involves identifying elements and molecules and their properties based on characteristics of the lines present in their spectra.

 

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Last updated June 8, 2006