# Why does the amount of my mouthwash influence the colour?

When I only have a little mouthwash left, it's more of an aqua/baby blue colour. When it's full, it's a much more deep blue. Why does the amount of the liquid determine the colour? Doesn't seem like it would be an issue of concentration.

• Is it a different color when viewing thru the same volume? See beer's law :p Jul 3, 2016 at 23:59

This may be a phenomenon due to Beer's Law: the amount of light a material absorbs is related to the path length of the light.

Since we're looking at the liquid from above the one on the left is a length of, say, 2cm ....whereas the one on the right is a path length of, let's say, 15cm.

Since the light is traveling through a much shorter length when it's empty than when it's full the color appears lighter.... i.e. less light is absorbed.

Of course I can't see if this is the case from the picture. Try looking at the two solutions through the length... if they're the same darkness then it's a Beer's. If they're still different then something else is going on. (But I'm betting on it being Beer's.)

• 'through the same length'? missing word? Sep 20, 2016 at 11:00

Yes you need to use Beer's law to understand this. We define the optical density $OD= \epsilon [C] l$ where $\epsilon$ is the extinction coefficient (strength of absorption a property of the dye molecules), concentration of dye $[C]$ and l path-length.

From the Beer-Lambert law an optical density of 1 absorbs 90% of the light (at a particular wavelength), a value of 2 absorbs 99% of the light etc.

The important quantity in your observation is the path-length (unless of course you have diluted the solution), which is longer in the full bottle. The Beer-lambert law can be written as $I_{trans} = I_0 10^{-OD}$ where $I_0$ is the initial intensity, i.e. before entering the solution and that transmitted $I_{trans}$. This is the light you observe. Take some liquid from the full bottle and gradually add to a glass and observe what happens to the apparent colour.

• What's special about mouthwash? Why is $\epsilon \cdot C$ bigger for mouthwash than a glass of apple juice etc? Sep 20, 2016 at 11:04
• I'm not doubting Beer's law, I'm just curious about the difference between mouthwash (where this appears to be a noticeable effect) and other liquids (where I haven't noticed it afaik) Sep 20, 2016 at 11:05