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I am currently doing some work in Spectroscopy, and I was wondering how are absorbance, and transmittance related? Do they have a domain, and range, how to read some sample graphs.

I was recommended this book "Principles of Instrumental analysis" by Douglas A. Skoog, and I took some notes from the UV section, because I am working in the Terahertz range, and I would like to learn how to distinguish water peaks, or if there's water in the sample. I have taken a basic background in General Chemistry 1 in college, and Physics 1, and 2 as well.

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In spectroscopy, absorption of electromagnetic waves (light) by an atom or molecule excites a change in the internal energy of the atom or molecule. The excitation modes of an atom or molecule range from nuclear, electronic, vibrational, rotational, and translation in order of decreasing energy that is required to cause a change in the given energy.

When light travels through a bulk substance, any light that is not absorbed by causing an excitation mode is transmitted through the material.

When light travels from a medium of one refractive index to another, it is refracted by and can be reflected back from the interface. Reflection from metals is essentially a mode of absorption in bulk excitation of the free electrons in the metal followed by de-excitation with transmission of the light back out of the metal.

Consider a substance that has an incident intensity of light $I_o$. The sum of the relative amount of reflected light $R$, absorbed light $A$, and transmitted light $T$ must be unity.

$$ R + A + T = 1$$

In transmission mode spectroscopy with light going through a sample, we neglect reflection. Therefore $A + T = 1$. The ratio of transmitted light intensity $I$ to incident light intensity is the transmittance and the ratio of absorbed light intensity to incident is the absorbance. They are related as $T = I/I_o = (I_o - I_a)/I_o = 1 - A$.

The relative amount of light that is absorbed by a material as light travels through a path $dz$ is proportional to the number density of absorbing atoms or molecules $\rho_N$ (number per volume). This gives the differential from of the Beers law relationship.

$$\frac{dI}{I} = \alpha \rho_N dz $$

Therefore we find that for a sample with thickness $L$

$$ \ln A = \alpha \rho_N L$$

Finally, every mode of absorption has its own characteristic energy. Reference books and resources provide the information needed to assign the absorption peaks in spectroscopy to the specific excitation mode. This means that both $A$ and $T$ depend on the wavelength (or frequency) that is being used or measured.

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Light is either reflected, absorbed or transmitted. The degree to which is called reflectance, absorbance and transmittance. If the refractive indices of the materials are known these quantities can be calculated using Fresnel's equations. My advise is that you read for example Wikipedia articles with these keywords.

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