## Posts Tagged ‘Beer’s Law’

### Why is yellow food colouring red?

October 25, 2010

Why is yellow food colouring red?

Not an exposition, but a question. Why is yellow food colouring red?

While making a movie the other day, I purchased some yellow food colouring and some red food colouring. It wasn’t till I got it home that I was astonished to find that the yellow colouring was red! Even the bottle top was red!

Now I can begin to explain this for myself – I am not there yet – but I was surprised to say least. So while I try to understand this, can someone please explain to me ‘Why is yellow food colouring red?’

### UPDATE

My colleague Dave Lowe kindly sent me a link to a site which discusses a related problem . The answer has to do with the amount of light transmitted by the food colouring at different wavelengths. And it is also another example of something we touch upon in Protons for Breakfast, that the colour of an object depends three things:  the spectrum of light illuminating the object; the way light travels through or is reflected from the object; and the different sensitivity of our eyes.

Imagine the spectrum of white light shown above, and imagine that the food colouring molecules absorb all the high frequency light (which we perceive as blue), a middling amount of the middle wavelengths (which we perceive as yellowy-orange), and almost none of the low frequency light (which we perceive as red). Because white light has more of the middle wavelengths present, then even though the food colouring transmits a higher fraction of red light, thin layers or small amounts of the colouring appear yellow. But as the thickness of the food colouring increases, something unusual happens, something described as Beer’s law.

#### More thin layers making a thick layer: Since no blue light made it through the first layers, non will make through a thick layer. For each layer thickness, and additional 50% of the yellow light is absorbed. After 10 thin layers that amounts to  (1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 ) which is approximately one thousandth of the original yellow light. Nearly all the red light that was transmitted through the first layer and the second layers also makes it through the subsequent layers. So after many layers, the initial dominance of the yellow transmitted light is replaced by dominance of the red light light.

Illustration of Beer Lambert Law or Beer's Law