Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 23 - Ray Optics - Exercises and Problems - Page 692: 63

Answer

$15.1\;\rm cm$

Work Step by Step

We need to use the thin lenses equation of $$\dfrac{1}{s}+\dfrac{1}{s'}=\dfrac{1}{f}$$ We need to find the focal length by using the best-fit line. So, $$\dfrac{1}{s}=-\dfrac{1}{s'}+\dfrac{1}{f}$$ we can see that this formula is a straight-line formula $y=mx+b$ where $y=s^{-1}$, $x={s'}^{-1}$, $m=\rm{slope}=-1$, and $b=f^{-1}$. So after we plot the given data, the $y$-intercept will be equal to $$b=f^{-1}$$ So, $$f=\dfrac{1}{b}\tag 1$$ Noting that $s$ is the Bulb to lens distance, $s'$ is the image [screen] to lens distance. From the graph below, we can see that $$b=0.06626$$ Hence, $$f=0.06626^{-1}=\color{red}{\bf 15.1}\;\rm cm$$
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