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 24 - Optical Instruments - Exercises and Problems - Page 713: 11

Answer

The appropriate aperture diameter is $~~4.2~mm$

Work Step by Step

We can see the relationship between intensity, shutter speed, and f-number: $I \propto \frac{1}{t} \propto \frac{1}{(f-number)^2} = \frac{D^2}{f^2}$ Then: $D^2 \propto \frac{1}{t}$ We can find the appropriate aperture diameter $D_2$: $\frac{D_2^2}{D_1^2} = \frac{t_1}{t_2}$ $D_2^2 = (\frac{t_1}{t_2})~(D_1^2)$ $D_2 = (\sqrt{\frac{t_1}{t_2}})~(D_1)$ $D_2 = (\sqrt{\frac{1/125~s}{1/500~s}})~(3.0~mm)$ $D_2 = (\sqrt{2})~(3.0~mm)$ $D_2 = 4.2~mm$ The appropriate aperture diameter is $~~4.2~mm$
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