Fresnel's Equations/ Normal Incidence/ R and T coefficients.

Click For Summary

Homework Help Overview

The discussion revolves around applying Fresnel's equations at normal incidence to determine the ratio of refractive indices between two non-magnetic, non-conducting dielectric materials. The original poster expresses confusion regarding the implications of non-magnetic and non-conducting properties on permeability and permittivity, particularly in relation to the refractive index calculation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how non-magnetic and non-conducting properties affect the calculation of refractive indices, questioning whether these properties imply using the permeability and permittivity of free space. Other participants provide insights on the definitions of non-conducting materials and clarify the relationship between Fresnel coefficients and wave amplitudes.

Discussion Status

The discussion is ongoing, with participants exploring the definitions and implications of material properties on the problem at hand. Some guidance has been offered regarding the treatment of permeability and permittivity, but no consensus has been reached on the original poster's confusion about the concepts involved.

Contextual Notes

There is a mention of specific values for relative permittivity and the conditions of equal energy transmission and reflection, which may influence the interpretation of the problem. The original poster's uncertainty about key concepts suggests that further clarification may be necessary.

binbagsss
Messages
1,291
Reaction score
12
The question asks to use Fresnel's equations at normal incidence to find the ratio of the refractive indexes of the two materials. We are told equal energy is transmitted and reflected and that both media are non-magnetic and non-conducting dielectrics.

So I know that the ratio of Er/Ei and Et/Ei are the same for this case, regardless of whether the electromagnetic wave is parallel or perpendicular to the planar interface .

In this case, we are also told both media are non-magnetic. So the ratios of Er/Ei and Et/Ei simplify further as ui=ut=u0

(where Ei is the incident electric field , Er reflected, ui the permeability of the media with the incident beam etc.)

Now I am then asked if one of the media has a relative permittivity of 16 ,what is the refractive index of the other media?

This is probably a stupid question, but if non-magnetic means to take the permeability to be the permeability of free space, then doesn't non-conducting mean to take the permittivity to be the permittivy of free space?

And n = (\epsilon_{r}\mu_{r})^{\frac{1}{2}}. So they would both be equal and equal 1 which is obviously wrong.

( I am able to follow the working to get the correct expression for the ratio of the refractive indexes, I'm just missing some key concepts clearly...)

Many thanks for any assistance !
 
Physics news on Phys.org
Nonconducting means no sustained electric current can be established. The medium may still be polarized which gives it a permittivity different than vacuum permittivity.
 
Thanks for your reply. Am i correct in thinking that non-magnetic means to take the permeability to be the permeability of free space ?
 
You can take the permeability equal to that of free space.

Note, that the Fresnel coefficients relate the amplitudes, both of transmitted and reflected waves to that of the incident wave, but the transmitted energy is not equal to the square of the transmission coefficient.

ehild
 
Deriving Clebsch Gordan Coefficents.

...
sorry, i don't think you can delete your posts
 
Last edited:

Similar threads

Total Internal Reflection and Transmitted Wavelength
  • · Replies 1 ·
Replies
1
Views
1K
Proving that the incident intensity is not the same as the sum of others
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad EM Power transmitted from one region to another (normal incidence)
  • · Replies 6 ·
Replies
6
Views
2K
Are the Fresnel coefficients equal for E and B fields?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Finding the Fresnel coefficients from interface conditions
  • · Replies 2 ·
Replies
2
Views
9K
Finding Fresnel coefficients from the interface conditions
  • · Replies 1 ·
Replies
1
Views
2K
How Is Incident Power Transmitted When Light Hits Water?
  • · Replies 3 ·
Replies
3
Views
2K
High School Calculating non-dielectric reflectance without using complex numbers
  • · Replies 6 ·
Replies
6
Views
1K
What Is the Angle of Incidence for Light to Emerge Parallel from a Sphere?
  • · Replies 2 ·
Replies
2
Views
3K
Planar wave normally incident on dielectric boundary
  • · Replies 1 ·
Replies
1
Views
2K