Penetration Depth What are the values to plug in equation? And what are the step

Question

Penetration Depth
What are the values to plug in equation? And what are the steps? Part ATR Penetration Depth 2 (sin20 n wavenumber np refractive index of ATR crystal n, refractive index of sample 0 effective angle of incidence nm, 195 nm, and 190 nm, respectively, have been chosen to be measured for Hzo content using the FTIR+AIM with an ATR objective. For these analyses, H20 will be measured by monitoring the fundamental OH stretching vibration at 3550 cm". Determine the penetration depth for each sample. 3550 cm 10.000 3550 cm 2.817 pm 45 2.817 1/2 8 (0.5 n sample ATR Crystal nn Forsterite 4 1.6 Anorthite Enstatite 4 1.65 HINT: The wavelength used in the calculations is in um (microns), therefore the answer will be in microns. Will the forsterite sample be thick enough for analysis? Will the anorthite sample be thick enough for analysis? Will the enstatite sample be thick enough for analysis?

Explanation / Answer

For a given sample,

the penetration depth can be calculated with formula,

dp = 2.817 / 8(0.5-nsp2)1/2

where

dp = penetration depth

nsp = ns/np

Now,

For forsterite,

Sample thickness = 200nm

nsp = ns/np

nsp = 1.7/4 = 0.425

dp = 2.817 / 8(0.5-nsp2)1/2

dp = 2.817 / 8(0.5-0.4252)1/2

dp = 0.1983 m = 198.3 nm

Since penetration depth is less than sample thickness, Fosterite sample will be thick enough for analysis.

For anorthite,

Sample thickness = 195nm

nsp = ns/np

nsp = 1.6/4 = 0.4

dp = 2.817 / 8(0.5-nsp2)1/2

dp = 2.817 / 8(0.5-0.42)1/2

dp = 0.1922 m = 192.2 nm

Since penetration depth is less than sample thickness, Anorthite sample will be thick enough for analysis.

For enstatite,

Sample thickness = 190nm

nsp = ns/np

nsp = 1.65/4 = 0.4125

dp = 2.817 / 8(0.5-nsp2)1/2

dp = 2.817 / 8(0.5-0.41252)1/2

dp = 0.1952 m = 195.2 nm

Since penetration depth is more than sample thickness, Enstatite sample will not be thick enough for analysis.

Sample ATR Crystal np ns nsp dp(m) Forsterite Ge 4 1.7 0.425 0.1983 Anorthite Ge 4 1.6 0.4 0.1922 Enstatite Ge 4 1.65 0.4125 0.1952

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