[Bidagdha_TADIR]

Suppose I dissolve a small particle of PABA in methanol and run the solution produced in UV-Visible spectrophotometer at 200-400nm. I will get a absorbance vs. wavelength spectrum. There is no way I can construct a logarithm epsilon vs. wavelength spectrum in this situation.

On the other hand, if I run a solution of 10^-6M PABA solution, I will still get a absorbance vs. wavelength spectrum but I can construct a logarithm epsilon vs. wavelength spectrum by changing the absorbance scale to log(absorbance/10^-6) scale.

Did I got this, or have I made a mistake?

[Corribus]

You can only calculate the extinction coefficient if you know the concentration, so you are correct. However it's not really appropriate to do this with only a single concentration value. You need at least three, to make sure you are in the linear range.