Optical density and dilution

[Arjan.]

The problem: how to determine the optical density of a diluted sample
Hi, i work on algae and bioenergy and i have a question about the OD.

I have to determine the optical density of about 400 samples. Some samples however are too "dense" for the photospectrometer, that is they have an optical density greater than the range of the spectrometer (>4,5 OD)

In order to determine the optical density of these samples I diluted them.

So for example:
The original sample has an OD > 4,5, which is too high for the machine
So it was diluted.
0,5 ml of the sample were taken and 3,0 ml distilled H2O were added.
The OD of the diluted sample was measured
The OD of this sample is 1,58.

Question
What is the optical density of the original sample?


2. Relevant equations

http://upload.wikimedia.org/wikipedia/commons/0/04/Beer_lambert.png

The Lamber-Beer equation says:

Absorbance = extinctioncoefficient x length of path x concentration

Optical density = log ( I0/I1)
Absorbance = log ( I1/I0)

Links: http://en.wikipedia.org/wiki/Optical_density
http://en.wikipedia.org/wiki/Beer-Lambert_law




3. The attempt at a solution

In the example above i diluted 7 times, so the optical density is 7 x 1,58 = 11,06

[Ygggdrasil]

Your answer is correct. The OD of the original sample is the OD of the diluted sample * the dilution factor.

[Redbelly98]

This doesn't make sense to me. OD is a base-10 logarithm scale. So for example, if you dilute by 10x then the diluted OD will be 1 less than (not 1/10th) of the undiluted OD.

The original OD should be
1.58 + log(7)
= 1.58 + 0.85
=2.43

However, you should have been able to measure OD 2.43 in the original sample.

[Ygggdrasil]

According to the Beer Lambert Law (http://en.wikipedia.org/wiki/Beer_lambert_law), the absorbance of a sample (aka optical density) varies linearly with the concentration for sufficiently dilute samples.

[Redbelly98]

Deleted post ... just realized an error in how I was thinking about all this.

[Borek]

varies linearly with the concentration for sufficiently dilute samples.

And this word "sufficiently" is the only reason why I have not posted earlier that Arjan procedure was correct...