Stokes relations arise by visualizing the rays running backwards in time, so that there are two incident waves of amplitudes and A portion of is reflected and a portion transmitted at the interface. Let and be the coefficients for the wave incident from below. The reflected portion is then and the transmitted portion is . Similarly, the incoming wave of amplitude splits into waves of amplitudes and . It must follow that
and 
A portion of 
and 
be the coefficients for the wave incident from below. The reflected portion is then 
and the transmitted portion is 
.
and 
. It must follow that 
