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