# Homework Help: Knowing the Refractive Index of a Prism using Microwave Transmitter

1. Dec 8, 2012

### ecastro

1. The problem statement, all variables and given/known data
A prism of 90-45-45 was placed between a microwave receiver and transmitter. What steps should I take to know the index of refraction of the prism given that its material is not transparent to microwave?

I positioned the prism so that a side of the prism is perpendicular to the beam (one of the legs), so I could have a 0 degree data, but how will I further improve this process (having a data graph for example). I did try to rotate the prism, however, I have no way of knowing how to measure the refracted beam inside the prism because this is what is happening:

Last edited by a moderator: May 6, 2017
2. Dec 8, 2012

### ehild

If the material of the prism is not transparent to microwaves, you do not get any output microwave signal. The prism reflects some part of the incident radiation and absorb all that enters into it. You can measure the ratio of the reflected intensity with respect to the incident one and use Fresnel's equations for reflectance in terms of the refractive index, angle of incidence and polarization.

http://en.wikipedia.org/wiki/Fresnel_equations.

The easiest method to get the refractive index would be finding the Brewster angle.

ehild

3. Dec 9, 2012

### ecastro

Sorry, what I mean by transparent is that microwave doesn't just pass through it. :P The wave is refracted in some way. Can the Fresnel Equations applicable if this is the case?

4. Dec 9, 2012

### ehild

The waves always partly reflect and partly refract from an interface between two different materials. So the wave never passes across unchanged. The problem says that the prism material is not transparent. That means the prism absorbs all the energy of the refracted wave. The detector can measure only the intensity of the reflected wave.
Fresnel equations are valid both for reflection and refraction at an interface.

ehild

5. Dec 10, 2012

### ecastro

If the material is indeed transparent to microwave that the wave is refracted and reflected. How will I know the refractive index if I have no way of knowing the angle of transmittance inside the prism (if there is a way, how could it be done).

6. Dec 11, 2012

### ehild

Read the text of the problem:
Arrange the prism that the reflected wave reaches the receiver.

ehild

7. Dec 19, 2012

### ecastro

Thanks. I just passed my report, I just hope that may gathered data are acceptable.