Fresnel equation reflection calculator


This page contains a calculator to work out the effects of reflection when light moves through parallel interfaces between materials of different refractive indices. It uses Snell's Law to work out how the beam is refracted then Fresnel's equations to work out the reflections. Calculations are done individually for light polarized perpendicular (S) to and parallel (P) to the plane containing the incident beam and the normal to the interfaces assuming half the power in each polarization then the results are summed to get the effect for un-polarized light.

A known limitation of this calculator is that it does not take into account the possibility of multiple reflections. For example, with a single sheet of glass some light will be reflected from the outer surface and will be lost immediately. Some light will be reflected from the inner surface. Of this, most will pass back out through the outer surface and be lost but a portion will be reflected back. Of that some will penetrate the inner surface and some will be reflected again. The net effect is that a small amount more light will actually pass than is shown by these calculations. Further, in the case where a layer is thin these multiple reflections will interfere constructively and/or destructively, as is used in anti-reflective coatings, resulting in additional effects not dealt with by this calculator.

In deciding how much reliance to put on the results from this page you should consider that, though I vaguely remember Snell's Law from school physics, I only know of Fresnel's equations from the Wikipedia article referenced above. I've done the odd bits of JavaScript before but part of the purpose of this page is to help me cement and extend my limited knowledge. In other words, you'd be a bit silly to take the results shown here too seriously. If you break your legs as a result of using this information don't come running to me.

On the other hand, if you can suggest any corrections or improvements then please get in touch.

Fill in the refractive indices of the layers to be modeled in the input boxes below then press Calc to get a table of the reflected amounts of light for different angles of incidence. The default refractive indices are for double glazing with the glass having a refractive index of 1.5 and the air or argon or whatever having a refractive index of 1.0. The links below set up some common cases which might also be of interest.

In the table, hover the cursor over the individual column titles for a bit more of an explanation.

Input data

Refractive indices of layers:

Polarization of the incident light: