How to determine accurate mass of beta-carotene from beta-carotene extract using spectrophotometer?

In [this video](https://www.youtube.com/user/ekuchemlab/videos), a beta carotene extract(the first yellow fraction) is obtained from $0.5$ g of presumably raw spinach. The extract contains beta-carotene dissolved in organic solvent (9 to 1 hexane to ethyl acetate solution). My question is how to determine mass of beta-carotene contained in this extract using spectrophotometer. I am doing a research that requires quantification of beta-carotene in specific mass of spinach but my school does not offer advanced equipment such as HPLC. 




The video [Beta-Carotene from Spinach](https://www.youtube.com/watch?v=Tf3_2GFPC50) from the Eastern Kentucky University Chemistry Lab describes the extraction and purification of $\beta$-carotene by flash chromatography, a method developed by [W. Clark Still](https://en.wikipedia.org/wiki/W._Clark_Still) in [*J. Org. Chem.*, **1978**, *43*, 2923-2925](http://dx.doi.org/10.1021/jo00408a041). 


Note that this is **not** HPLC, but preparative column chromatography (on silica) under pressure. It's an awesome method every organic chemist should be familiar with. 


Typically, you would run the (flash) chromatography, collect your material in test tubes, check the composition of every test tube by thin-layer chromatography (TLC), combine identical fractions and evaporate the solvent (on a rotary evaporator). This will give you the total mass of each fraction. 


In order to have a closer look at these fractions, prepare solutions of defined concentrations in *n*-hexane and examine them in a UV spectrometer. In *n*-hexane, the molar extinction coefficient $\epsilon$ of $\beta$-carotene is $139500~\mathrm{L\,cm^{-1}\,mol^{-1}}$ at $\lambda = 451~\mathrm{nm}$.


Supposed that your solutions are not too concentrated, their absorbance will obey to the *Lambert-Beer* law.


$$E\_\lambda = \epsilon\cdot c \cdot d $$


This means that the absorbance is proportional to the concentration of the absorbing species and that the concentration can be calculated from the absorbance $\mathrm{E\_\lambda}$, the thickness $d$ of the cuvette and the molar extinction coefficient $\epsilon$.


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