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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
All textbooksGiancoli Douglas 5th editionCh. 33 - Lenses and Optical InstrumentsProblem 98
Chapter 32, Problem 98

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.)

Verified step by step guidance
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Step 1: Understand the problem. The man initially uses +2.5 D lenses to read at a distance of 25 cm. Ten years later, he needs to hold the paper 32 cm away to see clearly with the same lenses. The goal is to determine the new lens power required for him to read at 25 cm again.
Step 2: Recall the lens formula: 1/f = 1/d_o + 1/d_i, where f is the focal length of the lens, d_o is the object distance (distance from the paper to the lens), and d_i is the image distance (distance from the lens to the eye).
Step 3: Convert the lens power to focal length using the relationship P = 100/f, where P is the lens power in diopters and f is the focal length in cm. For the initial lens power of +2.5 D, calculate the focal length.
Step 4: Use the lens formula to find the new lens power required for the man to read at 25 cm. Set d_o = 25 cm and solve for P using the relationship P = 100/f. Ensure you account for the fact that the image distance d_i has changed due to the man's vision change over time.
Step 5: Substitute the values into the equations and simplify to find the new lens power. This will give the diopter value of the lenses required for the man to read at 25 cm again.

Key Concepts

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

Lens Power

Lens power, measured in diopters (D), is the reciprocal of the focal length in meters. It indicates how strongly a lens converges or diverges light. A positive power indicates a converging lens, which is used for correcting hyperopia (farsightedness), while a negative power indicates a diverging lens for myopia (nearsightedness). Understanding lens power is crucial for determining the appropriate corrective lenses needed for clear vision at specific distances.
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Accommodation

Accommodation is the eye's ability to change its focus from distant to near objects by altering the shape of the lens. As people age, the lens becomes less flexible, reducing accommodation ability, which often necessitates the use of reading glasses. In this scenario, the man's changing ability to focus on near objects over time illustrates the need for adjustments in lens power to maintain clear vision.

Lens Formula

The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens, expressed as 1/f = 1/v - 1/u. This formula is essential for calculating the necessary adjustments in lens power based on the distance at which an object is held. By applying this formula, one can determine the new focal length required for the lenses to provide clear vision at the specified distance.
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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

The focal length f of a converging lens can be found by placing an object of known size at various locations in front of the lens and measuring the resulting real-image distances dᵢ and their associated magnifications m (minus sign indicates that image is inverted). The data taken in such an experiment are given here:



(a) Show algebraically that a graph of m vs. dᵢ should produce a straight line. What are the theoretically expected values for the slope and the y-intercept of this line? [Hint: dₒ is not constant.] (b) Using the data above, graph m vs. dᵢ and show that a straight line does indeed result. Use the slope of this line to determine the focal length of the lens. Does the y-intercept of your plot have the expected value?

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Textbook Question

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?

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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