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UltravioletPhotography

Electromagnetic absorption by water


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Andy Perrin
Stefano please don’t use lambda for both attenuation length and wavelength in the same document. Also log base e should be ln().
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ex (in the second formula) is the entire base. Maybe my formulas can be simplified, if someone can tell me. Also in the third one the base is e with an exponent.
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The problem is that symbols are recycled in physics. In this case we have two lambdas, one for the wavelength and the other one for the attenuation length. Should I change the symbols?
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perhaps use "Mu" for linear attenuation??

The lowercase version may generate confusion with "µm" (maybe not). Should I use another symbol not present in the document?
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Andy Perrin

µ won't create any confusion with micrometers. The base of a logarithm shouldn't have any variables like x in it. If you do, you should be rewriting it differently, but in this case I think you have simply done it wrong. Remember, e is a number like π. e^x is a function.

 

ln(x) = loge(x).

 

My suggestions would be:

 

post-94-0-85577400-1592605003.png

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The problem is that symbols are recycled in physics. In this case we have two lambdas, one for the wavelength and the other one for the attenuation length. Should I change the symbols?

 

This reminds me of how to find a chem-physics person in a room. Ask what new (nu) and they or I will answer c/lambda.

 

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µ won't create any confusion with micrometers. The base of a logarithm shouldn't have any variables like x in it. If you do, you should be rewriting it differently, but in this case I think you have simply done it wrong. Remember, e is a number like π. e^x is a function.

 

ln(x) = loge(x).

 

My suggestions would be:

 

post-94-0-85577400-1592605003.png

Thanks Andy, they were so simple to obtain! I always do simple things in a too complicated way. I just had to do ln on both sides and than rearrange things. What I instead did was to separate the components of the exponent, and that led to my not-so-nice (but still working) formulas (I tested them). I don't know why sometimes I can't see a simple solution, even when I have it in front of my eyes.
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Tomorrow I will fix a few things... thank you all for the suggestions.

 

Again, tell me if there is something else to fix, even minor things.

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Maybe I am thick, but "Also remember that a m-1 simply means a times in one meter. The length in meter is the reciprocal of a (1/a). If µ = 100 m-1, it means that µ = 0.01 m, or 1 cm." makes no sense. How can a length have the reciprocal of a length as a unit? I think I get what you're intending to say (in a colloquial way), but "m-1" in science is the reciprocal of a metre and used for the wavenumber (https://en.wikipedia.org/wiki/Wavenumber), for example. IMHO, you'd better not use "100 m-1" but rather "10-2 m".
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Andy Perrin
StephanN, mu is meters here. Not 1/m. It is the attenuation length. Alpha is the absorption coefficient which is in 1/m units. Alpha = 1/mu.
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m-1 is not the length (although correlated), but something different. The length says how much units (meters, for example) are contained in a "length". The other thing says how much lengths are contained in a unit. (Yes, I know you know it). I wrote it to make things easier for people not used to this writing. It is another way to write a length, if you will.

 

I had another idea: should I specify the differences between water vapor, liquid water and ice?

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Andy Perrin

Stefano, you still have some problems up there. You are using µ for attenuation length (m) in some places but as absorption coefficient (typically called alpha) (m^-1) in other places. You can't use it for both.

 

Is there any way you could let me edit this?

 

If µ = 100 m-1, it means that µ = 0.01 m, or 1 cm.

That's an example where you used two units for the same quantity in one sentence.

 

Correct this (and all similar errors) to:

 

If a = 100 m-1, it means that µ = 0.01 m, or 1 cm.

 

Or you can send it to me and I'll fix it for you if that's easier.

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It is the same for me (I can edit myself). If you will modify it, do you mean to send you the text, and then you will send me back the edited version? Or, can Andrea give you the ability to modify it? I fear links will break if I copy-paste them.
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Andy Perrin
Yeah use the Greek. As long as you are clear feel free to edit yourself. Otherwise I meant to send me the text.
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Keep in mind that I don't have a source for my text, I am writing it directly here. So what you see posted is the actual text.
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Sorry about my wrong way of putting it. Actually, what I couldn't get over was exactly the thing that Andy mentioned: You can't have two different units for the same quantity in an equation, and using the same letter for two different quantities (in the same context! Of course, in physics and mathematics, symbols must be reused, but never in the same set of equations) is also a foolproof way into all sorts of misunderstandings :smile:
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Today (later) I will fix a few things... my post gets better every time. It must be correct, written the right way.
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Did I insist too much on the difference between "µ" and "α"?

Also (again) should I talk (briefly) about the differences between the three states of matter (of water), that is water vapour, liquid water and ice?

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Ops, seems like I wrote “µ” in italic... will fix that...

 

...just noticed that the style of this symbol depends on the device (maybe the OS) on which you see it. It isn't written in italic.

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