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Beer's law relates absorbance to concentration. The "width" of the sample is part of the equation. I'm wondering why the height or diameter of the beam of light is not included as a factor. Or perhaps the height/diameter does affect the absorbance but can be factored out later. In other words would the absorbance change if the only thing varied is the height or diameter of the light beam; say if the height or diameter is doubled.

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Absorbance is a relative measure, Beer's law is $I_{trans}=I_0e^{-\epsilon [c]\ell}$ so that you have to measure both the transmitted light $I_{trans}$ and the amount when there is no solute in the sample cell $I_0$. Thus is does not matter how big or small your beam is assuming always that it all passes properly through the sample cell and the solution, i.e. not clipped by the cell or messed up by the miniscus etc. The beam size etc does not matter (unless you are using a high powered laser and I assume you are not) because all this is taken into account when you measure $I_0$.

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  • $\begingroup$ So, if I understand you correctly; if the beam height is changed, then $I_trans$ and $I_0$ will change as well. However, they will change in the same proportion, so when $I_trans$ is divided by $I_0$ the result is the same as if the beam height hadn't been changed. $\endgroup$
    – rdemyan
    Jan 20, 2023 at 17:41
  • $\begingroup$ @rdemyan, Yes you are right. As long as the beam is still passing through the solution, your understanding is correct. We cannot use a beam which is wider than the container width. In fact if you have a spectrophotometer, insert a piece of white paper and see how the beam shape looks like, by setting the spectrophotometer to blue or green wavelength (450 nm or 540 nm) $\endgroup$
    – AChem
    Jan 21, 2023 at 2:26
  • $\begingroup$ I should add that fluorescence is not measure via Beers law, it is just the number of photons counted at each wavelength. The fluorescence yield is tricky to get accurately but can be found most easily by comparison with a standard compound whose yield is known. $\endgroup$
    – porphyrin
    Jan 21, 2023 at 8:22
  • $\begingroup$ A larger beam diameter might help increase the SNR under some circumstances. $\endgroup$
    – datenheim
    Jan 21, 2023 at 22:49
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Beer's law relates absorbance to concentration. The "width" of the sample is part of the equation. I'm wondering why the height or diameter of the beam of light is not included as a factor.

It is not the width but the depth, i.e. the distance a beam of light travels through the sample. The height and width, or taken together the cross-sectional area or shape, are arbitrary as long as they same geometry is used for the blank.

In other words would the absorbance change if the only thing varied is the height or diameter of the light beam; say if the height or diameter is doubled.

You can take the same cuvette and place it in a cuvette-holder with a smaller aperture. The absorption will be the same. There will be more noise because it is harder to measure the smaller intensity of light, however. Here is an example of an adapter that changes the cross-section of the beam that arrives at the detector:

enter image description here

height of light beam when measuring fluorescence or absorbance

For fluorescence, the signal is in arbitrary units. Again, if you compare two samples, the cuvette and cuvette-holder should be the same, otherwise you get a systematic error.

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    $\begingroup$ Thank you for the correction. I did say "width" but I meant "depth". $\endgroup$
    – rdemyan
    Jan 23, 2023 at 19:23

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