Reflection and refraction at an interface, Fresnel's formulas
This program can be used to observe the wave field of an electromagnetic wave during reflection and refraction at an interface (e.g. air-glass). Positive amplitude of the E-field is shown in blue and negative amplitude in green. Black means zero amplitude. In particular, the change in wavelength and direction of propagation during refraction, the interference of the incident and reflected wave in front of the surface and the evanescent field during total reflection can be seen very clearly. A diagram with the reflectivity as a function of the angle can be displayed for each of the set parameters (see Fresnel formulae). The angle of incidence, refractive indices of the two media, wavelength and polarization of the light can be freely selected. For better understanding, the incident and reflected rays can be displayed individually and the ray path can be shown.
Downloads
Operation
The program is started with the "Start" button and stopped with "Stop". The parameters can all be changed while the program is running. You can use the slider at the top left to set the angle of incidence of the light between 0° (vertical incidence) and 89° (extreme grazing incidence). The light always comes from the top left corner of the picture. The refractive indices of the two media can be set using the two sliders below. Only real refractive indices between 1.0 and 2.0 are permitted. The wavelength of the light is selected with the slider below. (The selection of the wavelength has no influence on the refractive index, as this is set separately). The Zoom slider is used to set the image section between 1µm x 1µm and 20µm x 20 µm. By ticking the boxes "Hide incoming wave" or "Hide reflected wave", one of the two waves in front of the interface can be hidden. In reality, both waves are present and interfere with each other. To understand the wave field in front of the interface, however, it is helpful to be able to look at the two partial waves individually. With the check mark at the bottom left, the beam path can be displayed as red lines together with the boundary surface as a white line. Under the menu item "Windows", a window can be opened in which the reflectivity is displayed as a function of the angle of incidence. In the diagram, the reflectivity at the current angle of incidence is shown as a red dot. The currently displayed image can be saved and printed as a graphic in the menu.
To observe total reflection, the refractive index of the upper medium must be greater than that of the lower medium, e.g. glass n=1.5 at the top and air n=1.0 at the bottom. Depending on the angle of incidence, a reflected and a refracted wave or only a reflected wave together with a wave field that is exponentially attenuated downwards, the so-called evanescent wave, is observed.
Numerical realization
The wave field is calculated analytically using Fresnel's formulae.