Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 25 - Optical Instruments - General Problems - Page 742: 71

Answer

The sunlight's intensity increased by a factor of 8.2.

Work Step by Step

The amount of light reaching the camera sensor is proportional to the intensity of sunlight, the area of the shutter opening, and the time that the shutter remains open. The area of the shutter opening is proportional to the square of the diameter, and inversely proportional to the square of the f-stop. Equate the two expressions, because the exposure is the same. Remember that the times are constant. $$\frac{I_1t}{(f-stop_1)^2}=\frac{I_2t}{(f-stop_2)^2}$$ Now solve for the ratio of the 2 intensities. $$\frac{I_2}{I_1}=\frac{(f-stop_2)^2}{(f-stop_1)^2}=\frac{16^2}{5.6^2}=8.2$$ The sunlight's intensity increased by a factor of 8.2.
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