# What is meant by dispersion without deviation

## Explanation of the term "dispersion"

 December 21, 2007 5:23 pm Registration date: 16 years ago Posts: 1,834
The refractive index (= the refractive index) of an optical medium, e.g. glass, is not the same for all wavelengths. DISPERSION of an optical medium means the dependence of its refractive index on the vacuum * wavelength of the radiation (mostly light). Normally, the refractive index decreases with increasing wavelength, i.e. in the light range from violet to blue, blue-green, green, yellow-green, yellow, orange, red and purple, with violet and blue at first a little faster, then gradually a little more slowly. The curve is therefore not a straight line that slopes evenly from left to right (= from short to long wavelengths), but rather a slightly sagging line that is initially a little steeper and then more and more flatter. Such a falling dispersion course is referred to as NORMAL DISPERSION.

However, there can also be irregularities in the course of the dispersion, specifically in the vicinity of wavelengths at which resonance effects occur in the medium, with strong absorption (up to opacity) taking place, e.g. in the case of water in the infrared range. If there are such irregularities, it is called ABNORMAL DISPERSION. The spelling “abnormal” (with r) for “anomalous” (without r) is not wrong, but not common in optics.

In order to have a simple indicator for the dispersion, the MAIN DISPERSION was defined as the difference (= the difference) between the refractive index nF for the wavelength 486.1 nm (blue Fraunhofer hydrogen line F, hence the letter F as the index of n , the symbol for wavelength) and the refractive index nC for the wavelength 656.3 nm (red Fraunhofer hydrogen line C). So the refractive indices for two wavelengths that are far apart in the spectrum have been chosen near the limits of the visible range.

Depending on the type of optical medium, e.g. depending on the type of glass, the dispersion curve can run higher or lower (the latter e.g. for ED glass, ED = extra-low dispersion), which is not expressed in the value of the above main dispersion, but rather by the main refractive index nd (this is the refractive index for the wavelength 587.6 nm (yellow Fraunhofer helium line d roughly in the middle of the visible spectral range). In addition, the dispersion curve can also be steeper or flatter regardless of its mean height, which is precisely expressed by the main dispersion: Flat course means small main dispersion, steep course means large main dispersion.

Finally, the dispersion curves can differ not only in terms of height (indicated by the main refractive index nd) and the slope or steepness (indicated by the main dispersion nF - nC), but also in terms of shape deviations. The term PART-DISPERSION was defined in order to characterize these and to be able to indicate them in numerical values. Like the main dispersion, it is basically defined as the difference between the refractive indices nx and ny for two wavelengths x and y, which, however, are not exactly defined as those of the F and C lines of hydrogen, but depending on the peculiarities of the individual Dispersion curves can be selected within the observed spectral range in such a way that the part of the curve (hence “partial” dispersion) is covered in which there is a significant deviation from the normal shape. The partial dispersion of an optical medium related to the wavelengths x and x is thus equal to nx - ny.

Then there is the RELATIVE PARTIAL DISPERSION, which, as can be seen from the preceding word “relative”, is a ratio of an (individual) partial dispersion to the (standardized) main dispersion. Thus, the relative partial dispersion of an optical medium related to the wavelengths x and y is equal to (nx - ny) / (nF - nC).

If one now determines the relative partial dispersion for different optical media (different types of glass) for the same pairs of wavelengths x and y, it turns out that the relative partial dispersion is in most cases almost exactly proportional to the Abbe number of the respective medium. If you enter the relative partial dispersion of the various media in a diagram as a numerical value on the y-axis against Abbe's number on the x-axis, you get a whole bunch of points that are almost arranged on a straight line. But there are also some optical media whose relative partial dispersion is not on or very close to this line, but further away from it. These media are then referred to as ANOMALY PARTIAL DISPERSION.

* Explanation of the vacuum wavelength in the first paragraph: Actually, it would be more sensible to refer to frequencies of the radiation instead of wavelengths, because they stay on the way through various optical media, i.e. air, glass type 1, air, glass type 2, air, etc. ., always the same, while the wavelength is shortened within optically dense media due to the reduced speed of propagation therein (which does not mean a change in "color", but to explain that would be another and also not entirely uncomplicated thing, which is about physiology instead Physics works). Since one normally prefers to use wavelengths rather than frequencies, at least for light (= radiation range within which our eye perceives the radiation), as is common in communications engineering, for example, one has to refer to the wavelength in a quasi "neutral" Refer to medium, and this neutral medium is the vacuum. In practice, however, you can usually take dry air with 0.03 vol .-% CO2 at 20 ° C at normal pressure at sea level; the deviation from the vacuum wavelength is very small and mostly negligible. All readers, who take it very carefully, should please think of “vacuum wavelength” in my above explanation whenever I only wrote “wavelength” for the sake of simplicity and better readability.

One more note on the spelling. Main dispersion and partial dispersion are each to be written as one word. To emphasize (almost like a subheading) I have written the explained term dispersion in capital letters and then again for easier readability (which always suffers from capital letters) against the spelling rules main and partial dispersion with hyphens as MAIN-DISPERSION or PART-DISPERSION.

I understand that the above explanation of all the terms dispersion will be a tough nut to crack for most readers of this forum. Since the question about the explanation of the "abnormal partial dispersion" has been asked here and has not been answered by anyone else so far, I have tried not to answer it too briefly and not too long, halfway understandable for non-experts and yet not physically wrong. But it's just a pretty tricky thing, and unfortunately I'm too stupid to explain it more simply. I beg your forbearance for this.

Walter E. Nice

I am a little surprised by your statement that you knew what "ano (r) male dispersion" means. Because your other questions and statements (especially on the subject of ED glass and the “normal glass” you assume at Leica, Swarovski and Zeiss) do not identify you as an optics expert. Rather, my guess is that you would have a subjective feeling of having a rough (but not necessarily correct) idea of ​​what anomalous dispersion might mean. Not least because of this, I have explained all the different terms of dispersion in the text above and not just the “anomalous partial dispersion” mentioned in your question.
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