(a) If one layer cuts out of the UV, then it must allow through. Of this, will be allowed through by a second layer. So, of the original quantity of UV the fraction allowed through by two layers will be:Therefore will have been cut out.
(b) Similarly, if there are layers, the fraction allowed through will be . And the fraction cut out will beSo we want the smallest integer value of n for which
If you understand how to take logs of both sides, you can solve this inequality that way. Or you can simply use your calculator until you get the answer. Either way, I think it's 11 layers.