I was asked an interesting question on Twitter today. Not Anita asked me “If I apply a SPF50 suncream to my face, then a SPF15 mineral foundation, what SPF protection do I have?”
It is an interesting question when you think about. People are mixing sunscreens every day. Do the two products blend and give you an SPF half way between the two, of 32.5. Or does the second one to be applied cancel out the first one, which would leave her with an SPF of only 15. Or does the bigger number trump the lower one?
My reply was that in theory the two sunscreens should be additive, so you would end up with an SPF of 65. That was a good enough answer for Twitter. But I thought it was interesting enough to do a blog post going into a bit more detail. Because when I said in theory, I was referring to a very specific theory.
The theory in question is the Beer Lambert Law, and it is a very old theory. As is often the case, the name is misleading. It wasn’t discovered by somebody called Beer Lambert. It wasn’t even discovered by two people called Beer and Lambert. it was in fact originally discovered way back in 1729 by Pierre Bougeur. Lambert simply quoted it later. Beer added a bit more detail in 1852. So what does this law state? It is simply that the amount of light absorbed by a material is proportional to its thickness, its absorbency and its concentration.
This might sound obvious, but in science being obvious isn’t enough. You need to test it out. And if possible, you need an equation to describe it. This is certainly possible in this case, and as equations go it is a pretty simple one. But being simple doesn’t stop it being very useful. The Beer Lambert relationship enabled chemists to work out a great deal of information simply by passing light through samples. In the twentieth century this became mechanised and systematic, and machines were built called spectrophotometers that could be used to do a lot of testing very quickly and easily. It became practical to do research into basic chemistry at a speed that would have astonished chemists from an earlier era.
To give one example, spectrophotometers could identify chemicals that had particularly strong absorption in the UV range. It would have taken a very long time to test every potential sunscreen ingredient by applying it to the skin of volunteers and wait for them to see how well it protected them. Placing a sample in the spectrophotometer gave you an answer in seconds.
But the Beer Lambert las also meant that once you knew the amount of UV light a particular agent absorbed, you could work out what concentration should work in the formulation – again saving a great deal of legwork.
And last of all, knowing the theory you can answer Not Anita’s question. All that from really quite a simple theory. It is surprising sometimes just how useful science can be.
Thanks to Bill Branson via Wikipedia Commons for releasing the copyright to his photo of a woman applying a sunscreen.