unstoppable
Dec12-08, 04:03 PM
1. The problem statement, all variables and given/known data
A uniform plane wave traveling in free space is incident obliquely at angle theta onto the surface of a prefectly conduction plane(a mirror). The resultant magnetic field vector is disovered to be zero at a distance s in front of the mirror.
(a) What is the lowest possible frequency omega of the wave if the incident wave polarization is TM?
(b) Why can the incident wave polarization not be TE?
2. Relevant equations
The fields in the dielectrics are
E=Eoexp(-jk1n*r)-Eoexp(+jk1 n*r)=-2jEosin(k1n*r)
H=Hexp(-jk1n*r)+Hoexp(jk1n*r)=2Hocos(k1 n*r)
E(r,t)=2*Eosin(k1n*r)sin(omega*t)
H(r,t)=2*Hocos(k1n*r)cos(omega*t)
NOTE:the n*r denotes the dot product of the position and the normal vector
3. The attempt at a solution
I made omega*t=theta and then I used Euler's equation e^j*theta, however I don't think what I'm doing is correct!
A uniform plane wave traveling in free space is incident obliquely at angle theta onto the surface of a prefectly conduction plane(a mirror). The resultant magnetic field vector is disovered to be zero at a distance s in front of the mirror.
(a) What is the lowest possible frequency omega of the wave if the incident wave polarization is TM?
(b) Why can the incident wave polarization not be TE?
2. Relevant equations
The fields in the dielectrics are
E=Eoexp(-jk1n*r)-Eoexp(+jk1 n*r)=-2jEosin(k1n*r)
H=Hexp(-jk1n*r)+Hoexp(jk1n*r)=2Hocos(k1 n*r)
E(r,t)=2*Eosin(k1n*r)sin(omega*t)
H(r,t)=2*Hocos(k1n*r)cos(omega*t)
NOTE:the n*r denotes the dot product of the position and the normal vector
3. The attempt at a solution
I made omega*t=theta and then I used Euler's equation e^j*theta, however I don't think what I'm doing is correct!