(a) Use conceptual arguments to show that the intensity of...

Name: Problem 6, Chapter 25: College Physics
Uploaded: 2021-04-13T14:26:30-08:00
Duration: 2 min 59 s
Channel: Ajay Singhal

(a) Use conceptual arguments to show that the intensity of light (energy per unit area per unit time) reaching the film in a camera is proportional to the square of the reciprocal of the $f$ -number as $$I \propto \frac{1}{(f / D)^{2}}$$ (b) The correct exposure time for a camera set to $f / 1.8$ is $(1 / 500)$ s. Calculate the correct exposure time if the $f-$ number is changed to $f / 4$ under the same lighting conditions. Note: "f/4," on a camera, means "an $f$ -number of $4 . "$

(a) Use conceptual arguments to show that the intensity of light (energy per unit area per unit time) reaching the film in a camera is proportional to the square of the reciprocal of the $f$ -number as
$$I \propto \frac{1}{(f / D)^{2}}$$
(b) The correct exposure time for a camera set to $f / 1.8$ is $(1 / 500)$ s. Calculate the correct exposure time if the $f-$ number is changed to $f / 4$ under the same lighting conditions. Note: "f/4," on a camera, means "an $f$ -number of $4 . "$

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Key Concepts

Exposure Time Adjustments

Exposure time represents the duration for which the film or sensor is exposed to light. When the aperture size is changed (via the f-number), the exposure time must be adjusted to maintain proper exposure. Specifically, if the aperture area decreases, a longer exposure is needed to compensate for the reduced light intensity.

Aperture Area and Light Intensity

The area of the aperture determines the quantity of light entering the camera and is proportional to the square of the aperture’s diameter. Since the f-number is inversely related to the aperture diameter, the intensity of light reaching the film or sensor is proportional to the square of the reciprocal of the f-number.

f-number

The f-number is the ratio of a lens’s focal length to the diameter of its aperture. It effectively characterizes how wide the aperture is; a lower f-number means a larger aperture that admits more light, while a higher f-number means a smaller aperture that admits less light.

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