# How does the Beer Lambert law work at non-normal incidences?

• warfreak131
In summary, the reflected light from a thin film of aluminum deposited on a glass substrate is 93% of the original light. The reflected light must be taken into account when calculating attenuation.
warfreak131
I want to calculate the intensity of a transmitted wave in a medium, but not at normal incidence. I want to consider the case of 45 degrees. What proportion of the intensity of the wave is lost by reflection?

Specifically I am looking at a the reflection off of a thin film of aluminum deposited on a glass substrate.

That's not so much a question about Lambert Beer. Rather you have to use the Fresnel equation
http://en.wikipedia.org/wiki/Fresnel_equations
with some expression for the complex index of refraction of aluminium, to first determine the amount of reflected light from the aluminium surface. The latter one can be found e.g. in the Handbook of physics.

Thanks Dr Du. Since my light source is going to be unpolarized, the total reflectance is going to be (Rs+Rp)/2. Since both Rs and Rp are dependent on n2, would I just use the real index of refraction to calculate the amount reflected, and then when calculating what is attenuated, use the complex part as well?

No, reflectivity also depends on the imaginary part,too.

Okay, so I calculated Rp+Rs / 2, and I got 93% reflectivity, but that doesn't take into account the thickness of the film. I think it's more appropriate as a way to model a thick film where practically nothing makes it through the aluminum film.

EDIT: Or is it just impossible, regardless of the film thickness?

Last edited:
93% reflectivity sounds at least reasonable. The remaining 7% will get either absorbed or transmitted. Given the thickness of the film and the angle of refraction you calculated, you can calculate the effective path length in the aluminium film and use Lambert Beer to calculate what reaches the lower surface. There you should take reflectivity into account again, to calculate the final intensity in the glas.

## 1. What is the Beer Lambert law?

The Beer Lambert law, also known as the Beer-Lambert-Bouguer law, is a relationship between the concentration of a substance in a solution and the amount of light that is absorbed by that solution. It is commonly used in spectrophotometry to quantify the concentration of a substance in a solution.

## 2. How does the Beer Lambert law work?

The Beer Lambert law states that the absorbance of a solution is directly proportional to the concentration of the absorbing substance and the path length of the light through the solution. This means that as the concentration of the substance increases, the absorbance also increases, and as the path length increases, the absorbance also increases.

## 3. What is the formula for the Beer Lambert law?

The formula for the Beer Lambert law is A = ɛcl, where A is the absorbance, ɛ is the molar absorptivity coefficient, c is the concentration of the substance, and l is the path length of the light through the solution. This formula can be rearranged to solve for any of the variables.

## 4. Does the Beer Lambert law work at non-normal incidences?

Yes, the Beer Lambert law can be applied at non-normal incidences, meaning that the light is not passing through the solution perpendicular to the surface. However, the path length of the light through the solution may need to be adjusted to account for the angle of incidence.

## 5. What are some limitations of the Beer Lambert law?

While the Beer Lambert law is a useful tool for quantifying the concentration of a substance in a solution, it does have some limitations. One major limitation is that it assumes that the light passing through the solution is monochromatic, meaning it has a single wavelength. Additionally, it assumes that the solution is free of any scattering or other interfering substances, which may not always be the case.

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