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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 5
Chapter 32, Problem 5

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?

Verified step by step guidance
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Step 1: Understand the problem and identify the relevant formula. This is a thin lens problem, and we will use the lens equation: 1f = 1do + 1di, where f is the focal length, do is the object distance, and di is the image distance.
Step 2: Rearrange the lens equation to solve for the image distance di: di = f∗do / (do - f). This will allow us to calculate the position of the lens for each object distance.
Step 3: For part (a), substitute the given values into the formula: f = 105 mm and do = 10.0 m (convert to mm: do = 10000 mm). Calculate di using the formula.
Step 4: Repeat the calculation for part (b) with do = 3.0 m (convert to mm: do = 3000 mm) and for part (c) with do = 1.0 m (convert to mm: do = 1000 mm).
Step 5: For part (d), determine the closest object distance by setting the image distance di to its maximum value of 132 mm (the maximum distance allowed between the lens and the sensor plane). Rearrange the lens equation to solve for do: do = f∗di / (di - f). Substitute f = 105 mm and di = 132 mm to find the closest object distance.

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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 focal length (f) of a lens to the object distance (u) and the image distance (v) through the equation 1/f = 1/u + 1/v. This formula is essential for determining how far the lens should be positioned from the sensor to achieve a sharp image of an object at a given distance.
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Lens Maker Equation

Thin Lens Approximation

The thin lens approximation assumes that the thickness of the lens is negligible compared to the distances involved. This simplification allows us to use the lens formula without accounting for lens thickness, making calculations more straightforward when dealing with ideal lenses.
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Thin Lens Equation

Magnification

Magnification is the ratio of the height of the image to the height of the object, and it can also be expressed as the negative ratio of the image distance to the object distance (M = -v/u). Understanding magnification helps in assessing how the size of the image changes with respect to the object distance, which is relevant when positioning the lens for different object distances.
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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

(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

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?