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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 97
Chapter 32, Problem 97

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?

Verified step by step guidance
1
Step 1: Recall the formula for the magnification of a telescope, which is given by \( M = \frac{f_o}{f_e} \), where \( f_o \) is the focal length of the objective lens and \( f_e \) is the focal length of the eyepiece lens. The objective lens is the one with the longer focal length, and the eyepiece lens is the one with the shorter focal length.
Step 2: Use the relationship between the power of a lens (in diopters) and its focal length (in meters): \( P = \frac{1}{f} \), where \( P \) is the power of the lens and \( f \) is the focal length. Rearrange this formula to find \( f = \frac{1}{P} \).
Step 3: Calculate the focal lengths of the two lenses. For the lens with power \( +2.0 \ \text{D} \), the focal length is \( f = \frac{1}{2.0} \ \text{m} \). For the lens with power \( +4.5 \ \text{D} \), the focal length is \( f = \frac{1}{4.5} \ \text{m} \).
Step 4: Identify which lens should be used as the objective and which as the eyepiece. The lens with the longer focal length (\( +2.0 \ \text{D} \)) should be used as the objective, and the lens with the shorter focal length (\( +4.5 \ \text{D} \)) should be used as the eyepiece.
Step 5: Substitute the focal lengths into the magnification formula \( M = \frac{f_o}{f_e} \). Use the calculated focal lengths from Step 3 to determine the maximum magnification possible. Simplify the expression to find the result.

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Key Concepts

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

Lens Power and Focal Length

The power of a lens, measured in diopters (D), is the reciprocal of its focal length in meters. A lens with a power of +2.0 D has a focal length of 0.5 meters, while a +4.5 D lens has a focal length of approximately 0.22 meters. Understanding lens power is crucial for determining how lenses can be combined to form optical devices like telescopes.
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Magnification in Telescopes

Magnification in telescopes is defined as the ratio of the focal lengths of the objective lens to the eyepiece lens. The maximum magnification achievable depends on the combination of these lenses. For a telescope, the objective lens gathers light and forms an image, while the eyepiece magnifies that image for viewing.
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Types of Lenses

There are two main types of lenses: converging (convex) and diverging (concave). In this scenario, both lenses from the reading glasses are converging lenses, which are used in telescopes to focus light. The choice of which lens to use as the eyepiece affects the overall magnification and clarity of the image produced by the telescope.
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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?

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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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