In textbook on optics by Pedrotti (and I think Fowles does the same) on page 493 it is said that:
kr=k_{r}r=k_{t}r
from which follows
(kk_{r})r=(kk_{t})r=(k_{r}k_{t})r=0,
where k, k_{r} and k_{t} are wave vectors of incident, reflected and transmitted wave.
Than Pedrotti concludes that k_{r} and k_{t} must lie in a plane determined by k and r. Must they?
Take, for example this:
k=(1,0,1), r=(1,0,0), k_{r}=(1,5,3), k_{t}=(1,2,1).
If we put this vectors in the equation above, we will get 0, but k_{r} and k_{t} don't lie in the plane determined by k and r, which is y=0 plane.
So I conclude that Pedrotti is wrong. Am I right or wrong to conclude that? If wrong, why?
