The lens equation says that if an object is placed at a Problem 7E Chapter 3.4

Statistics for Engineers and Scientists | 4th Edition

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Problem 7E

The lens equation says that if an object is placed at a distance p from a lens, and an image is formed at a distance q from the lens, then the focal length f satisfies the equation 1/f = 1/p+1/q. Assume that p = 2.3 ± 0.2 cm and q = 3.1 ± 0.2 cm.

a. Estimate f, and find the uncertainty in the estimate.

b. Which would provide a greater reduction in the uncertainty in f: reducing the uncertainty in p to 0.1 cm or reducing the uncertainty in q to 0.1 cm?

Step-by-Step Solution:

Step 1 of 3:

By lens equation the focal length of a lens satisfies the equation = . where p is the difference between the object and the lens and q is the difference between the lens and the image.

If  P= 2.3 cm and q= 3.1 0.2 cm we have to find :

The estimate of focal length f. And the uncertainty in the estimate.Which would provides a greater reduction in the uncertainty in f: reducing the uncertainty in p to 0.1 cm or reducing the uncertainty in q to 0.1 cm.

Step 2 of 3:

Here the focal length of a lens satisfies .

p= 2.3 0.2 cm , which means p= 2.3 , and the uncertainty .

q = 3.1 0.2 cm , which means q = 3.1 , and the uncertainty .

So the focal length of the lens

f = = =  1.320 cm

And = = = =     0.3295 = = = =     0.1814

So the uncertainty in the estimate is = =    0.075

Therefore the estimate of focal length is (1.320 0.075) cm. And the uncertainty in the estimate is 0.075 cm.

Step 3 of 3

ISBN: 9780073401331

This full solution covers the following key subjects: uncertainty, lens, equation, distance, reducing. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 7E from chapter: 3.4 was answered by Patricia, our top Statistics solution expert on 06/28/17, 11:15AM. The answer to “The lens equation says that if an object is placed at a distance p from a lens, and an image is formed at a distance q from the lens, then the focal length f satisfies the equation 1/f = 1/p+1/q. Assume that p = 2.3 ± 0.2 cm and q = 3.1 ± 0.2 cm.a. Estimate f, and find the uncertainty in the estimate.________________b. Which would provide a greater reduction in the uncertainty in f: reducing the uncertainty in p to 0.1 cm or reducing the uncertainty in q to 0.1 cm?” is broken down into a number of easy to follow steps, and 92 words. Statistics for Engineers and Scientists was written by Patricia and is associated to the ISBN: 9780073401331. Since the solution to 7E from 3.4 chapter was answered, more than 249 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4th.

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