In the article [How SPF Changes with How Much Sunscreen You Use](https://labmuffin.com/spf-changes-how-much-sunscreen-use/) (last updated Dec 29, 2017), the author says that it is disturbing that insufficient sunscreen (in theory) decreases protection exponentially: >The amount used in the sunscreen studies to determine SPF is $2$ milligrams of sunscreen per centimetre of skin. > >On average, **people apply only a quarter to a half of the recommended amount**, and in most studies, it’s closer to $0.5$ mg/cm². > >In physics, you’d expect protection to **decrease exponentially** with less sunscreen. This is based on a relationship called the Beer-Lambert law > >[![enter image description here][1]][1] > > it’s the middle of the graph that’s disturbing. > >**Applying half the recommended amount of sunscreen cannot give more than SPF $\mathbf{10}$**, even with SPF $50$ sunscreen! > >by $0.5$ mg/cm², we’re below SPF $3$ for all products. Does this mean that applying more sunscreen theoretically gives *increasing* marginal utility? Does the theory really contradict our intuition that the initial layer (of the recommended amount of sunscreen) is *more* beneficial, that is, make a greater difference, than any subsequent layer? [1]: https://i.sstatic.net/WMpct.png