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Ch. 33 - Lenses and Optical Instruments
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
Chapter 32, Problem 92

As early morning passed toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to change the f-number from f/5.6 to f/16. By what factor had the sunlight intensity increased during that time?

Verified step by step guidance
1
Understand the relationship between the f-number and light intensity: The f-number (or aperture) is inversely proportional to the square root of the light intensity. Specifically, the intensity of light is proportional to \( \frac{1}{f^2} \), where \( f \) is the f-number.
Identify the initial and final f-numbers: The initial f-number is \( f_1 = 5.6 \), and the final f-number is \( f_2 = 16 \).
Set up the ratio of intensities: The ratio of the initial intensity \( I_1 \) to the final intensity \( I_2 \) is given by \( \frac{I_1}{I_2} = \frac{f_2^2}{f_1^2} \).
Substitute the values of \( f_1 \) and \( f_2 \) into the formula: Replace \( f_1 \) with 5.6 and \( f_2 \) with 16 to calculate the factor by which the intensity has increased.
Simplify the expression: Perform the squaring and division to determine the factor \( \frac{I_2}{I_1} \), which represents the increase in sunlight intensity.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Exposure Triangle

The exposure triangle consists of three elements: aperture (f-number), shutter speed, and ISO. These elements work together to control the exposure of an image. A change in one element necessitates adjustments in the others to maintain the same exposure level. In this case, the photographer adjusted the aperture to compensate for increased light intensity.
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Aperture and f-numbers

Aperture refers to the opening in a camera lens that allows light to enter. It is measured in f-numbers (e.g., f/5.6, f/16), where a lower f-number indicates a larger opening and more light, while a higher f-number indicates a smaller opening and less light. Changing from f/5.6 to f/16 reduces the light entering the camera, requiring adjustments to maintain exposure.
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Light Intensity and Stops

Light intensity in photography is often measured in 'stops,' where each stop represents a doubling or halving of light. Adjusting the aperture from f/5.6 to f/16 is a change of three stops, meaning the light intensity has increased by a factor of eight (2^3). This relationship is crucial for understanding how changes in settings affect exposure.
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Related Practice
Textbook Question

An astronomical telescope, Fig. 33–36, produces an inverted image. One way to make a telescope that produces an upright image is to insert a third lens between the objective and the eyepiece, Fig. 33–39b. To have the same magnification, the non-inverting telescope will be longer. Suppose lenses of focal length 150 cm, 1.5 cm, and 10 cm are available. Where should these three lenses be placed to make a non-inverting telescope with magnification 100x?

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Textbook Question

A physicist lost in the mountains tries to make a telescope using the lenses from his reading glasses. They have powers of +2.0 D and +4.5 D, respectively.

(a) What maximum magnification telescope is possible?

(b) Which lens should be used as the eyepiece?

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Textbook Question

Figure 33–49 is a photograph of an eyeball with the image of a boy in a doorway. (a) Is the eye here acting as a lens or as a mirror? (b) Is the eye being viewed right side up or is the camera taking this photo upside down? (c) Explain, based on all possible images made by a convex mirror or lens.


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Textbook Question

(II) A planoconvex lens (Fig. 33–2a) has one flat surface and the other has R = 15.3 cm. This lens is used to view a red and yellow object which is 62.0 cm away from the lens. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens?

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Textbook Question

A 50-year-old man uses +2.5 D lenses to read a newspaper 25 cm away. Ten years later, he must hold the paper 32 cm away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 cm away? (Distances are measured from the lens.)

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Textbook Question

A series of polarizers are each rotated 10° from the previous polarizer. Unpolarized light is incident on this series of polarizers. How many polarizers does the light have to go through before it is 1/6 of its original intensity?

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