- #1
LCSphysicist
- 644
- 162
- Homework Statement
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- Relevant Equations
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Imagine that we have a transmitter of microwaves that radiates a linearly polarized wave whose E field is known to be parallel to the dipole direction. We wish to reflect as much energy as possible off the surface of a pond (having an index of refraction of 9.0). Find the necessary incident angle and comment on the orientation of the beam.
I have solved it, but since the textbook has no solutions on it i would like to know if you agree with my answer:
Since for electric field perpendicular to the plane of incidence $$r_{per} = sin^2(\Delta \theta)/sin^2(\sum \theta)$$
And for electric field parallel $$r_{par} = tan^2(\Delta \theta)/tan^2(\sum \theta)$$
We have $$r_{par} = tan^2(\Delta \theta)/tan^2(\sum \theta) = r_{per} cos^2(\sum \theta)/cos^2(\Delta \theta) < r_{per} $$
So, since we want to maximize the reflected energy, we should make the dipole perpendicular to the plane of incidence.
The problem is about the angle of incidence. My answer would be something like:
"To got maximum reflection energy, make the dipole perpendicular to the plane of incidence, so that the electric field is also perpendicular to the plane. About the angle, make the incident angle of the wave ##\theta \to \pi/2##.
What do you think?
I have solved it, but since the textbook has no solutions on it i would like to know if you agree with my answer:
Since for electric field perpendicular to the plane of incidence $$r_{per} = sin^2(\Delta \theta)/sin^2(\sum \theta)$$
And for electric field parallel $$r_{par} = tan^2(\Delta \theta)/tan^2(\sum \theta)$$
We have $$r_{par} = tan^2(\Delta \theta)/tan^2(\sum \theta) = r_{per} cos^2(\sum \theta)/cos^2(\Delta \theta) < r_{per} $$
So, since we want to maximize the reflected energy, we should make the dipole perpendicular to the plane of incidence.
The problem is about the angle of incidence. My answer would be something like:
"To got maximum reflection energy, make the dipole perpendicular to the plane of incidence, so that the electric field is also perpendicular to the plane. About the angle, make the incident angle of the wave ##\theta \to \pi/2##.
What do you think?