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 Post subject: Fraunhofer
PostPosted: Thu May 24, 2007 1:02 am 
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Reading old tutorial chat sessions, I find lots of interesting topics. As I've told Doos repeatedly, I am amazed that peeps expend so much effort self-teaching physics. If only I could get my students to do the same!

If everyone already understands the topic of this post... sorry, I'll come back and delete it after my holiday. The inspiration for this post came from http://yey.be/yglogs/yglog48.cgi .

The topic I hope to clear up here is the (average) index of refraction n, versus the indices nB, nD, and nG. Briefly, the index of refraction of a particular material is the ratio of the speed of light in vacuum (3*10^8 m/s) divided by the speed of light in the material of interest. Index of refraction is always larger than one (light average speed is always slower in any material than it is in vacuum) and rarely greater than 2 (light doesn't slow down much for anyone, diamond being an exception).

The indices nB, nD, and nG refer to the speed ratios at specific wavelengths of light (687 nm, 589 nm [actually there are two close together], and 431 nm [actually there may be three close together], respectively). The general index of refraction n is an average value of these three indices in materials where light is not greatly dispersed. Dispersion, again briefly, describes the difference between values for nB, nD, and nG... the greater the differences, the higher the dispersion.

In optics, for a piece of slag glass not particularly dispersive, a problem may only require the average value n, but for gems (which in general are much more highly dispersive than most transparent material) one needs to define a specific wavelength at which to measure index of refraction, and one may also want to characterize the dispersion (the fire, I guess y'all call it).

So a diamond, which is quite dispersive, exhibits quite different values for n at different wavelengths (homework question: what are the values of nB, nD, and nG for diamond?). But, and this is the point of this post, how were these particular wavelengths chosen? Well these particular wavelengths were identified by Fraunhofer as specific absorption lines appearing in the emission spectrum of sunlight.**

The sun's inner volume is a black-body radiator, which should produce a nice smooth spectrum. But the outer atmosphere of the sun (and the earth's atmosphere) contains atomic elements which absorb certain discrete wavelengths of light. Fraunhofer characterized the deepest of these absorption lines as A, B, C ... and so on, where A is the longest wavelength deep absorption, and B is the next longest wavelength deep absorption, and so on... Now, the A absorption line occurs around 759 nm, which to me is in the infrared. I have no clue how he spotted this line, I've never been able to see it. The B absorption line occurs in the visible red at the wavelength listed above. The D absorption line in the yellow is, by far, the deepest of the deep absorption lines, occurring at the wavelength listed above. The G absorption line is at the opposite, violet end of the visible spectrum at the wavelength listed above. As was eventually discovered, there are actually thousands of absorption lines in the sun's spectrum, but the deepest five or six are given capital letter designations.

The difference between nB and nG gives a thumbnail sketch of how dispersive a material is (values differing by 0.05 are moderately dispersive).

As was learned later on, these absorption lines were due to single atoms or diatomic molecules absorbing the blackbody light output of the sun's photosphere. As it happens, the Fraunhofer B line corresponds to an oxygen molecule transition (and thus arises from sunlight passing through the earth's atmosphere), the D line corresponds to a sodium doublet transition (for some reason beyond the discussion of this post, sodium is perfectly poised to absorb the maximum amount of the maximum light that the sun produces... it is almost too perfect... only mercury outdoes sodium's efficiency, but mercury absorbs and emits in the deep UV). Finally, the true G line of the sun arises because of an atomic calcium transition.

(Quick aside: my favorite Fraunhofer line is F, nicely situated in the cyan color range, almost as easy to observe in the spectroscope as the D lines)

In atomic emission lamps, instead of absorbing light, the atoms can emit light at these particular wavelengths. Thus a sodium spectral lamp, the most efficient visible light source, emits nearly monochromatic light at 589 nm. So that is why most refraction index measurements are made at nD.

And this is the origin of the wavelengths chosen for measuring indices of refraction. Similarly, a key indicator of the dispersion in a prism spectrometer is represented by the angular spread of C-F Fraunhofer lines.

Keywords for googling up in-depth readings: blackbody radiation, sodium D lines, C-F, H-alpha H-beta H-gamma, Balmer series, Mercury (Hg) fluorescent lamp, sodium (Na) spectral lamp, low pressure Na

**The emission spectrum of the sun shown in the wiki article was collected with an Ocean Optics spectrometer. These spectrometers are truly point-and-shoot... this guy collected the sun's spectrum from the blue sky through a pane of glass. His spectrometer is a couple generations behind the ones I am using to collect transmission spectra of gem material... but then, I don't have a spectrum appearing in a wiki, do I?


Last edited by Brian on Thu May 24, 2007 1:33 am, edited 1 time in total.

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PostPosted: Thu May 24, 2007 1:30 am 
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I don't have a spectrum appearing in a wiki, do I?


Not yet, but if you wanted to add them to the GP wiki, along with the sort of info/ explanations that you just posted here, drop a line to Doos who can create an account for you. :D


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PostPosted: Thu May 24, 2007 1:45 am 
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I dont see any reason to come back and delete this. Does anyone else??

While we are on the subject of lettered spectral lines and dispersions if anyone is going to get real technical about dispersion they might want to be aware that in our little gemological world we measure dispersion from B to G but apparently everyone else in engineering and academia measure it from C-F especially when using polarized light microscopes.

Also manufacturers of glass and optical materials specify the dispersion of the glass using something called an Abbe V number named for its divisor the great german optical scientist Ernst Abbe who with Carl Zeiss more or less invented the modern microscope. The Abbe V number is calculated using C-F dispersion.

The C line is 656.3nm and the F line is 486 so CF dispersion is less than BG dispersion. This might be news you can use if you are going to develop a new line of paste faceted stones or you feel sure that world needs another critical angle refractometer or you are going to redesign the Hastings triplet.

You can see more about it here:
http://en.wikipedia.org/wiki/Abbe_number


Also since Frauenhoefer was a spectroscopy guy I will take this opportunity to tell people to go here, yet again:

http://ioannis.virtualcomposer2000.com/ ... ments.html


I know Brian is in agreement with this and its just in case you havent seen it the other three times we've posted it. Scroll past the numbers and look at his descriptions of different kines of light with graphs that are easy to understand.


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PostPosted: Thu May 24, 2007 1:12 pm 
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Please don't delete this, Brian :shock: . Yours is a great explanation of dispersion and spectral lines ... hey, even I understood it :D .

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PostPosted: Thu May 24, 2007 3:16 pm 
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Hello Brian,

Your post is excellent and remember me when I was playing with my refractometer after the reading of this article from the australian gemologist:
http://www.australiangemmologist.com.au ... ersion.pdf

It is possible to determine the apparent dispersion (not the absolute dispersion) from one refractometer in particular.
Mesuring the refractive index of a substance (i.e. gem) with a 656 nm red light (like the red laser from the informatic mouse => line C), and the F line (486 nm) that it can be furniched by a Hbeta filter used for astronomia.
The difference between the refractive index at C line and Fline give the "apparent disperssion C to F for this refractometer" .

For exemple: quartz:
Under red light 656 nm (C) Ne=1.559 No=1.549
Under the 486 nm light (F) Ne=1.529 No=1.519
Apparent C-F disperssion of this quartz with this refractometer (in this case it is a duplex II from GIA) = 0.030 for Ne and idem for No

Utility of this technique??.
hum.. :? ... not very usefull in fact.. :oops:
because a lot of overlaped values and the data can not be compared with data from an other refractometer :(

But we have play with light, filter, PC mouse, refractometer .. :P

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PostPosted: Thu May 24, 2007 4:19 pm 
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Hi,

Nice essay Brian and thank you for the compliment.
We indeed need the input of a physicist to help us overcome our self-studies and give us indepth information on topics that we are interested in and struggle with.
There are many topics that we have studied and not really understand. Although we don't need the information on a daily base, some of us hunger for them. We need to keep our brains working in order to feel alive. Plus as Annie always says, "kill the subject".
Apparent easy subjects become more easy when you know the ins and outs.

As Africanuck said, please feel free to contribute to the project. We need this kind of information.

Gemça and G4lab are correct, we use the B-G interval for dispersion instead of the C-F one and the article Gemça posted is a great read.
Does anyone have an answer why the B-G interval was chosen? Or was it as Brian says, most minerals don't show such a high dispersion.


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PostPosted: Wed May 30, 2007 12:18 am 
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Oh thanks, flattery will get y'all everywhere with me :wink: . I've learned my lesson, I won't delete what I usually think is useless information.

I, myself, cannot figure out why gemmos would choose the B-G wavelengths for describing dispersion, but there are literally hundreds of reasons to choose the C-F wavelengths. I'll quickly point out a couple of the reasons behind the C-F choice.

Firstly, you can use a hydrogen spectral lamp that only produces light at the C and F wavelengths (along with one or two dim lines deep in the violet). Unlike a sodium spectral lamp, though, a hydrogen spectral lamp isn't very bright.

In contrast, I've never seen a calcium spectral lamp for producing the G wavelength light.

If you need a bright source of C and F wavelength light, halogen light produces significant intensity at the C and F wavelengths, and you just need to filter out all the other wavelengths. These light filters, known as Halpha (red, C) and Hbeta (cyan, F), are commonly available from astronomy sources.

In contrast, halogen light doesn't produce much intensity at the G wavelength. So even with an appropriate filter, a halogen light would be a weak source for G wavelength light.


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PostPosted: Mon Jun 04, 2007 3:24 pm 
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In contrast, I've never seen a calcium spectral lamp for producing the G wavelength light.

Hollow Cathode Lamps for Atomic Absorbtion spectrosopy are available both new and surplus pretty easily.

That 687 line is more difficult.


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