Dielectrics and Phase Shifts

Simple worked example - 3GHz EM radiation is incident on a sheet of material with εr  =  2.7 and a hole in it. What is the sheet thickness that makes the waves (a) and (b) in phase when they emerge from the sheet?

The Powerpoint image shows the example and the simualtion animates it (as well as allowing frequency and direlectric constant to be varied.

The simulation also shows what would happen if the waves thropugh air and dielectric were recombined after passing through.  The dielectric thickness and/or constant can be adusted to cause them to add, to cancel, and everything in between.  This is the principle that, in more comlpex form and with multiple reflections, allows anto-reflection coatings to be added to (for example) camera lenses.