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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 1b
Chapter 32, Problem 1b

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

Verified step by step guidance
1
Start by identifying the lens formula, which relates the focal length \( f \), the object distance \( d_o \), and the image distance \( d_i \): \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \).
Substitute the given values into the lens formula. Here, \( f = 235 \ \text{mm} \) and \( d_i = 373 \ \text{mm} \): \( \frac{1}{235} = \frac{1}{d_o} + \frac{1}{373} \).
Rearrange the equation to isolate \( \frac{1}{d_o} \): \( \frac{1}{d_o} = \frac{1}{235} - \frac{1}{373} \).
Simplify the right-hand side by finding a common denominator for the fractions and performing the subtraction: \( \frac{1}{d_o} = \frac{373 - 235}{235 \cdot 373} \).
Finally, take the reciprocal of \( \frac{1}{d_o} \) to find \( d_o \), the object distance: \( d_o = \frac{235 \cdot 373}{373 - 235} \).

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Key Concepts

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

Lens Formula

The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens. It is expressed as 1/f = 1/v + 1/u. This equation is fundamental for solving problems involving lenses, as it allows us to find one of the distances when the other two are known.
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Lens Maker Equation

Sign Convention for Lenses

In optics, the sign convention is crucial for correctly applying the lens formula. For a converging lens, the focal length (f) is positive, the object distance (u) is negative if the object is on the same side as the incoming light, and the image distance (v) is positive if the image is on the opposite side of the lens. Understanding this convention helps avoid errors in calculations.
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Ray Diagrams for Converging Lenses

Converging Lens

A converging lens, or convex lens, is thicker at the center than at the edges and focuses parallel rays of light to a point known as the focal point. The focal length is the distance from the lens to this focal point. Converging lenses are commonly used in applications such as cameras and magnifying glasses, making them essential in optics.
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Related Practice
Textbook Question

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?

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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

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?