Solution Found!
In the article “Temperature-Dependent Optical Constants of
Chapter 3, Problem 10E(choose chapter or problem)
In the article “Temperature-Dependent Optical Constants of Water Ice in the Near Infrared: New Results and Critical Review of the Available Measurements” (B. Rajaram, D. Glandorf, et al., Applied Optics, 2001:4449–4462), the imaginary index of refraction of water ice is presented for various frequencies and temperatures. At a frequency of \(372.1\mathrm{\ cm}^{-1}\) and a temperature of 166 K, the index is estimated to be 0.00116. At the same frequency and at a temperature of 196 K, the index is estimated to be 0.00129. The uncertainty is reported to be \(10^{-4}\) for each of these two estimated indices. The ratio of the indices is estimated to be 0.00116/0.00129 = 0.899. Find the uncertainty in this ratio.
Equation Transcription:
Text Transcription:
372.1 cm^-1
10^-4
Questions & Answers
QUESTION:
In the article “Temperature-Dependent Optical Constants of Water Ice in the Near Infrared: New Results and Critical Review of the Available Measurements” (B. Rajaram, D. Glandorf, et al., Applied Optics, 2001:4449–4462), the imaginary index of refraction of water ice is presented for various frequencies and temperatures. At a frequency of \(372.1\mathrm{\ cm}^{-1}\) and a temperature of 166 K, the index is estimated to be 0.00116. At the same frequency and at a temperature of 196 K, the index is estimated to be 0.00129. The uncertainty is reported to be \(10^{-4}\) for each of these two estimated indices. The ratio of the indices is estimated to be 0.00116/0.00129 = 0.899. Find the uncertainty in this ratio.
Equation Transcription:
Text Transcription:
372.1 cm^-1
10^-4
ANSWER:Solution 10E
Step1 of 3:
We have a frequency of 372.1 cm-1 and a temperature of 166 K. the index is estimated to be 0.00116. and the same frequency and at a temperature of 196 K, the index is estimated to be 0.00129.
That is
And also we have uncertainties .
Let r =
=
= 0.8992
We need to find the uncertainty of r.
Step2 of 3:
Consider the ratio
r =
Differentiate above equation with respect to “” then
=
=
=