The given electric field is:
(x,y,z,t)=E0eiko[(x+y+z)−ct]We can rewrite this as:
(x,y,z,t)=E0eiko[(++)⋅−ct] where
=x+y+z is the position vector. This represents a plane wave propagating in the direction of
++.
The wave vector is given by:
=ko(++) The magnitude of the wave vector is:
k=||=ko√3The speed of the wave in the medium is given by:
v=‌=‌=‌The refractive index of the medium is given by:
n=‌=√3 Since the electric field is polarized in the
x−z plane, the polarization vector
must be a linear combination of
and
. To ensure the polarization is in the
x−z plane, and considering the wave is propagating along
++, the polarization vector must be perpendicular to the direction of propagation. Thus:
=‌Therefore, the correct options are:
Option B:
=‌;v=‌.
Option C: Refractive index of the medium is
√3.