An electromagnetic wave reaching an interface is partially reflected, partially refracted. The fraction of it that gets refracted, i.e. the transmission coefficient, and the fraction of it that gets reflected, i.e. the reflection coefficient, depend on a number of things:
- the refractive indices of both media,
- the incidence angle, and
- the polarization of the light.
Although the frequency of the electromagnetic wave does not come up explicitly here, it does implicitly through the refractive index, which varies with frequency, a phenomenon known as dispersion.
Once you have figured the refractive indices of your media for a given frequency, all you need is Fresnel's Equations to figure out what happens to your waves. At each reflection, only a fraction of the incident light will be reflected, and the fraction will be different for different polarizations. So the light after the first reflection will be less strong, and polarized differently, than before reflecting, and the differences will pile up after a few reflections.
Furthermore, if your reflections are not isolated, but happen between parallel surfaces, you can have interference between the various incident, refracted and reflected beams, leading to a further dependency of the outcome on wavelength. This is what makes soap bubbles iridescent, for example.
There really is no shorter answer to your question other than: find out what the refractive index for your frequency of choice is, work out the details, find out what happens...