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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 7
Chapter 32, Problem 7

It is desired to magnify reading material by a factor of 3.0 x when a book is placed 9.0 cm behind a lens.
(a) Draw a ray diagram and describe the type of image this would be.
(b) What type of lens is needed?
(c) What is the power of the lens in diopters?

Verified step by step guidance
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To solve this problem, we first need to understand the relationship between the magnification (M), the object distance (d_o), and the image distance (d_i). The magnification is given by the formula: M = -dido. Here, M = 3.0, and d_o = 9.0 cm.
Rearrange the magnification formula to solve for the image distance (d_i): di = -M × do. Substitute the given values to find d_i.
Next, use the lens equation to find the focal length (f) of the lens. The lens equation is: 1f = 1do + 1di. Substitute the values of d_o and d_i into this equation to calculate f.
Determine the type of lens needed. Since the magnification is positive and the image is virtual (as indicated by the negative sign in d_i), the lens must be a converging lens (convex lens).
Finally, calculate the power of the lens in diopters using the formula: P = 100f, where f is in centimeters. Convert f to meters before substituting into the formula to find the power in diopters.

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Key Concepts

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

Magnification

Magnification is the ratio of the height of the image to the height of the object. In optics, it also relates to the distance of the object and the image from the lens. A magnification factor of 3.0 means the image will be three times larger than the object. Understanding this concept is crucial for determining the characteristics of the image formed by the lens.
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Lens Types

Lenses can be classified as converging (convex) or diverging (concave). A converging lens can produce a magnified image when the object is placed within its focal length, while a diverging lens always produces a virtual, smaller image. Identifying the correct type of lens is essential for achieving the desired magnification and image characteristics.
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Lens Power

The power of a lens, measured in diopters, is the reciprocal of its focal length in meters. A positive power indicates a converging lens, while a negative power indicates a diverging lens. Calculating the power is important for understanding how strong the lens needs to be to achieve the desired magnification and image distance.
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Related Practice
Textbook Question

(II) In a film projector, the film acts as the object whose image is projected on a screen (Fig. 33–46). If a 105-mm-focal-length lens is to project an image on a screen 22.5 m away, how far from the lens should the film be? If the film is 24 mm wide, how wide will the picture be on the screen?

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Textbook Question

(III) A bright object is placed on one side of a converging lens of focal length f, and a white screen for viewing the image is on the opposite side. The distance dT = di + do between the object and the screen is kept fixed, but the lens can be moved. Determine a formula for the distance between the two lens positions in part (a), and the ratio of the image sizes.

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Textbook Question

A 105-mm-focal-length lens is used to focus an image on the sensor of a camera. The maximum distance allowed between the lens and the sensor plane is 132 mm.

(a) How far in front of the sensor should the lens (assumed thin) be positioned if the object to be photographed is 10.0 m away? (b) 3.0 m away? (c) 1.0 m away?

(d) What is the closest object this lens could photograph sharply?

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Textbook Question

A sharp image is located 373 mm behind a 235-mm-focal-length converging lens. Find the object distance by calculation.

Textbook Question

An object is located 1.35 m from an 8.0-D lens. By how much does the image move if the object is moved (a) 0.90 m closer to the lens, and (b) 0.90 m farther from the lens?