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In the article “Temperature-Dependent Optical Constants of

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 10E Chapter 3.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 10E

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 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.

Step-by-Step Solution:
Step 1 of 3

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

                                     

                                            =

                                            =

                                            =

                                            =

                                            = 775.1937

Hence, = 775.1937.

Again consider the ratio

r =    

 Differentiate above equation with respect to “” then

                                     

                                            =

 ...

Step 2 of 3

Chapter 3.4, Problem 10E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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In the article “Temperature-Dependent Optical Constants of

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