# Fresnel Equations | Refractive Index Interface

• xiaoipower
In summary, a user is seeking clarification on the Fresnel equations for a refractive index interface. They explain that the equations involve an incoming normal plane wave and two materials with different refractive indices. The user is unsure if the incident and reflected terms should be added or subtracted. They ask for thoughts and mention that the coefficients can be found by solving for the boundary conditions.
xiaoipower
Hi guys!

Was wondering if anyone was confident with Fresnel equations for a refractive index interface. From what I understand:

Assume incoming normal plane wave traveling in z-direction and polarised in x plane.

Assume z=0 is the plane that separates two materials: n_1 and n_2 (refractive index)

I think the Fresnel solution for the wave should go:

Ex = (for z>0) exp(-i*k0*n_1*z)+r*exp(i*k0*n_1*z)

(for z<0) t*exp(-i*k0*n_2*z)

the RED term representing the normal incident component and the GREEN term represents the reflected component which only exist in the n_1 half

and the BLUE term representing the transmitted component which only exists in the n_2 half.

I am uncertain about if I should be adding both the incident and reflected term (for z>0) as long as they are traveling in different directions or if I need to subtract them. i.e. should it be RED+GREEN or RED-GREEN? As I already have defined them to travel in opposite directions.

Any thoughts?

Many thanks!

You find the coefficients by solving for the boundary conditions at the surface between the two media. This can be found in any textbook on electrodynamics or optics.

## 1. What are the Fresnel equations?

The Fresnel equations are a set of mathematical equations that describe the behavior of light when it passes through an interface between two different materials with different refractive indices.

## 2. What is the refractive index?

The refractive index is a measure of how much a material can bend or refract light. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material.

## 3. How do the Fresnel equations predict the behavior of light at an interface?

The Fresnel equations take into account the incident angle of light, the refractive indices of the materials, and the polarization of the light to predict the amount of light that will be reflected and transmitted at the interface.

## 4. What is the critical angle in the context of the Fresnel equations?

The critical angle is the angle of incidence at which light will be completely internally reflected instead of being transmitted through the interface. This occurs when the refractive index of the incident material is lower than the refractive index of the material it is entering.

## 5. What practical applications do the Fresnel equations have?

The Fresnel equations have many practical applications, such as in the design of lenses, prisms, and other optical devices. They are also used in the fields of optics, photonics, and telecommunications to understand and manipulate the behavior of light at interfaces.

Replies
6
Views
766
Replies
1
Views
349
Replies
3
Views
1K
Replies
1
Views
159
Replies
5
Views
22K
Replies
5
Views
8K
Replies
1
Views
768
Replies
1
Views
1K
Replies
2
Views
9K
Replies
6
Views
5K