# Reflection loss during absorption spectroscopy

1. May 4, 2010

### 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