In the blog post How SPF Changes with How Much Sunscreen You 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
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.
So, applying more sunscreen gives increasing marginal utility? But, when applying the recommended amount of sunscreen, shouldn't the initial layer be more beneficial (make a greater difference) than any subsequent layer?
