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Refer to Exercise 8. Assume the critical angle is measured

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

Solution for problem 18E Chapter 3.3

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 18E

Refer to Exercise 8. Assume the critical angle is measured to be 0.90 ± 0.01 rad. Estimate the refractive index and find the relative uncertainty the estimate.

Exercise 8: The refractive index n of a piece of glass is related to the critical angle  by n = 1/sin. Assume that the critical angle is measured to be 0.700.02 rad. Estimate the refractive index, and find the uncertainty in the estimate.

Step-by-Step Solution:

Solution:

Step 1 of 1:

Given the refractive index n of a piece of glass is related to the critical angle by

.

We assume that the critical angle is measured to be rad.

Now we have to estimate refractive index and the uncertainty in the estimate.

Our goal is:

We need to estimate refractive index and the uncertainty in the estimate.

Now we have to find the estimate the refractive index.

Let the refractive index n of a piece of glass is related to the critical angle is

Here .

Then, the uncertainty in the estimate is

We are differentiating with respect to .

     

     

     

Then we know that .

Therefore the uncertainty in the estimate is 1.0259.


Step 2 of 1

Chapter 3.3, Problem 18E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The answer to “Refer to Exercise 8. Assume the critical angle is measured to be 0.90 ± 0.01 rad. Estimate the refractive index and find the relative uncertainty the estimate.Exercise 8: The refractive index n of a piece of glass is related to the critical angle by n = 1/sin. Assume that the critical angle is measured to be 0.700.02 rad. Estimate the refractive index, and find the uncertainty in the estimate.” is broken down into a number of easy to follow steps, and 69 words. The full step-by-step solution to problem: 18E from chapter: 3.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: estimate, index, critical, angle, exercise. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Since the solution to 18E from 3.3 chapter was answered, more than 294 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331.

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Refer to Exercise 8. Assume the critical angle is measured