Reflection loss during absorption spectroscopy

[jm518]

An isotropic solid has a refractive index of 10 at low frequencies. A 10 um thick platelet of this solid with perfectly polished planes shows two absorption bands in optical transmission. These bands, corrected for reflection, have a (negative) Gaussian shape. They occur at frequencies of 3x1012 and 1014 Hz, respectively. The maximum light absorption is 50 and 90% respectively. Calculate the transmission spectrum vs frequency including reflection losses.

I have been stuck on this problem all week. I assumed that the absorption of 50 and 90% is able to be converted to 50 and 10% transmission at the two frequencies respectivley. Then I determined the reflectance using Fresnel's law, (n2-n1)^2/(n2+n1)^2, to be 0.67 and therefore the transmittance to be 0.33. Assuming that only one internal reflection occurs in the platelet I calculated the amount of transmission that came through the platelet was 0.109.

I am stuck on how the thickness plays into the equation and how to use the information I have to determine the reflection losses from the transmissions. I am thinking that the beer-lambert law comes into affect somewhere, I/Io = exp(-ux), and also that I should use the kramers kronig transform, but I am unsure how to do that. Any thoughts would be helpful.

Thanks

 

[eljose79]

for your post! It looks like you have made a good start in your calculations. To determine the transmission spectrum vs frequency, you will need to consider the thickness of the platelet and how it affects the absorption and reflection of light at different frequencies.

First, let's review the basics of the Beer-Lambert law. This law states that the amount of light absorbed by a material is directly proportional to the thickness of the material and the concentration of the absorbing species. In this case, the thickness of the platelet is given as 10 um, and the concentration of the absorbing species is not specified. However, we can assume that the concentration is constant throughout the platelet.

Next, let's consider the reflection losses. As you mentioned, the Fresnel equations can be used to calculate the reflectance at the interfaces of the platelet. However, since there are two interfaces (top and bottom), we need to consider the reflections at both interfaces. This means that the overall reflectance will be the product of the individual reflectances at each interface. In this case, the overall reflectance would be 0.67 * 0.67 = 0.4489.

Now, to determine the transmission spectrum vs frequency, we need to consider the overall transmission of light through the platelet at different frequencies. This can be calculated using the Beer-Lambert law, but we also need to take into account the reflection losses. This can be done by multiplying the transmittance (0.33) by the overall reflectance (0.4489), resulting in a total transmission of 0.148. This means that 14.8% of the incident light will be transmitted through the platelet.

To determine the transmission spectrum, we can plot the percentage of transmitted light at different frequencies. Since we know that the maximum light absorption occurs at 50% and 90% for the two absorption bands, we can use this information to determine the shape of the transmission spectrum. For example, at a frequency of 3x1012 Hz, the transmission would be (100-50)% * 0.148 = 7.4%. Similarly, at a frequency of 1014 Hz, the transmission would be (100-90)% * 0.148 = 1.48%.

Using this approach, we can plot the transmission spectrum vs frequency, taking into account the thickness of the platelet and the reflection losses. The resulting plot should show two peaks