P grow as lower powers.
There is however, a catch. P terms dominate near the place where one material changes to another. P terms, we'll get the transmission coefficient incorrect, although everything would be quite fine everywhere else except at the boundary. The problem is just that of focusing a slide projector. There is a small range of knob positions over which no one can notice any difference, and a larger range over which the people in the back row are not disturbed by misfocus.