# How is reflectivity of a surface determined?

1. Nov 24, 2005

### newbie7.07

I have no real experience in this subject and wanted to ask, can the amount of reflection (in terms of electromagnetic waves) of a substance be determined without physical testing?

2. Nov 24, 2005

### Dr Transport

If you have the indicies of refraction, yes.

3. Nov 24, 2005

### mezarashi

Yup, the reflectivity of an interface can be expressed through Fresnel's equations... which are from Maxwell's equations:

Just FYI (for normal incidence):

$$\Gamma = \frac{n_1 - n_2}{n_2 + n_1}$$

where gamma represents the reflection coefficient.

Last edited: Nov 24, 2005
4. Nov 24, 2005

### newbie7.07

Ummmmm...
What do you plug in for n1 & n2

5. Nov 24, 2005

### mezarashi

The index of refraction of medium 1 (original) and medium 2 (new). Usually air is n1 and n2 is glass.

Incident and reflected powers
$$P(reflected) = \Gamma^2 P(incident)$$

6. Nov 24, 2005

### newbie7.07

Oh. Actually I was wondering how you determine refractive index without testing. Sorry.

7. Nov 24, 2005

### mezarashi

The indices of refraction of optical materials are well tabulated.

Last edited: Nov 24, 2005
8. Nov 24, 2005

### dlgoff

The index or refraction is the ratio of the speed of light in a vacuum to the speed in the medium. To find the speed in the medium you need the materials relative permeability and permittivity. And that is found by measurment. Permeability and permittivity of a vacuum come from Maxwell's equations.

Regards

9. Nov 25, 2005

### Pieter Kuiper

One can calculate optical properties ab initio (with band structure calculations) but it is difficult to get good agreement with experiment.

10. Nov 25, 2005

### Dr Transport

What is the material????
If you have a crystalline structure, yes, calculate using the band structure all of the material poperties you want. As Pieter has said, you will have great difficulties getting agreement with experimental evidence.

If the material is amorphous, like a glass, lots of luck. I am not an amorphous material expert, but I'd be very suprised if you can get an answer in general.

dt