Power transmission and dielectric constant

[cesarsalad]

How do I find the reflectivity of a combination of ice on top of water(infinite half-space) as a function of the thickness of ice? I know how to find it for each material, it's just rho = ((root(dielectric constant)-1)/(root(dielectric constant)+1) )^2. I'm given dielectric constants for both. I'm pretty sure we have to calculate the emissivity of the top layer of ice, the emissivity of the underlying water, combine them together somehow, and reflectivity = 1 - emissivity.
There is no attenuation, and the thickness varies from 0 to the wavelength. So it's related to the phase shift somehow.
But I don't know how to calculate how much power goes from the sun, let's say, through the ice to the water and how it's related to the thickness of the ice. Does anyone know where I can find such an equation?

 

[Astronuc]

First of all, is the light at some angle - important for determining reflectance (and transmission).

Think about the fact that there are 3 media, and so 2 interfaces, 1 and 2.

At media interface 1, the incident light, I, is split. Say the amount that is reflected is I_r1 = r₁I, so the transmitted light intensity I_t1 = (1-r₁)I.

Now some of that light is reflected at the ice-water interface, I_r2=r₂I_t1= r₂ (1-r₁)I.

OK, but now the light reflected from the 2nd interface must pass through interface 1 again. So work out that equation, and think about the fact that remaining light is going from water to air, rather than air to water.

Then can you write r₁ and r₂ in terms of the dielectric properties (and thickness of ice as applicable)?

What light that emerges from the ice can be added to the reflected light to get the total intensity.

 

[cesarsalad]

Hi,

Thank you

There are going to be an infinite number of reflections. These reflections add up as an infinite series. For example, the total reflection is the reflection from the ice + one that went through the layer once + one that went through the layer twice + etc. What I'm having trouble figuring out is just how.. I know the layer thickness changes the phase, but how, and what does this have to do with the total reflectivitiy? btw, the wave is incident straight down (normal incidence)

EDIT: nevermind.. i figured it out. the phase changes like e^(i*k*d)