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A certain type of film requires an exposure time of 0.010 s with an $f / 11$ lens setting. Another type of film requires twice the light energy to produce the same level of exposure. What $f$ -number does the second type of film need with the 0.010 -s exposure time?

Name: Problem 7, Chapter 25: College Physics
Uploaded: 2020-03-28T20:14:30-08:00
Duration: 3 min 42 s
Channel: Netra Sharma
Description: A certain type of film requires an exposure time of 0.010 s with an f / 11 lens setting. Another type of film requires twice the light energy to produce the same level of exposure. What f -number does the second type of film need with the 0.010 -s exposure time?

   A certain type of film requires an exposure time of 0.010 s with an $f / 11$ lens setting. Another type of film requires twice the light energy to produce the same level of exposure. What $f$ -number does the second type of film need with the 0.010 -s exposure time?

College Physics

Raymond A. Serway,… 11th Edition

Chapter 25, Problem 7

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Solved by Expert Netra Sharma

03/28/2020

Step 1

The exposure time for film 1 is given as $t_1 = 0.010$ s and the $f$-number is $f_1 = 11$. Film 2 requires twice the light energy to produce the same level of exposure, and we want to find the $f$-number $f_2$ for film 2 with the same exposure time $t_2 = 0.010$ Show more…

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A certain type of film requires an exposure time of 0.010 s with an $f / 11$ lens setting. Another type of film requires twice the light energy to produce the same level of exposure. What $f$ -number does the second type of film need with the 0.010 -s exposure time?

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Key Concepts

Aperture (f-number) and Inverse Square Relationship

The f-number of a lens is a measure of the size of the aperture relative to the focal length and directly affects the amount of light reaching the sensor or film. Since the light admitted is proportional to the area of the aperture, and the area is inversely proportional to the square of the f-number, small changes in the f-number result in significant changes in light intensity.

Exposure Energy and Compensation

Exposure energy is the total amount of light that reaches the film or sensor, determined by both the exposure time and the size of the aperture. When a film requires twice the light energy for an equivalent exposure, if the shutter speed remains constant, the only way to increase the light intake is by enlarging the aperture. Due to the inverse square relationship, doubling the light energy requires reducing the f-number by a factor of the square root of two.

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