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Ch 34: Geometric Optics
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 34: Geometric OpticsProblem 50b
Chapter 33, Problem 50b

You wish to project the image of a slide on a screen 9.00 m from the lens of a slide projector. If the dimensions of the picture on a 35 mm color slide are 24 mm ✖ 36 mm, what is the minimum size of the projector screen required to accommodate the image?

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Determine the magnification (M) of the image using the lens formula and the given distances. The magnification is given by \( M = \frac{d_i}{d_o} \), where \( d_i \) is the image distance (9.00 m or 9000 mm) and \( d_o \) is the object distance (distance from the slide to the lens).
Calculate the dimensions of the projected image on the screen using the magnification. The width of the image is \( M \times 36 \ \text{mm} \), and the height of the image is \( M \times 24 \ \text{mm} \).
Convert the dimensions of the projected image from millimeters to meters by dividing by 1000, as the screen size is typically measured in meters.
Determine the minimum size of the projector screen required by considering the larger of the two dimensions (width or height) and ensuring the screen can accommodate both dimensions.
Summarize the result by stating the minimum dimensions of the screen in meters, ensuring it is large enough to display the entire projected image.

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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 process of enlarging the appearance of an object through optical devices like lenses. It is defined as the ratio of the image size to the object size. In this context, understanding how the slide's dimensions relate to the projected image size on the screen is crucial for determining the minimum screen size needed.
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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 how the slide's image is formed by the projector lens, which directly influences the size of the projected image on the screen.
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Aspect Ratio

Aspect ratio is the ratio of the width to the height of an image or screen. For the slide dimensions given (24 mm by 36 mm), calculating the aspect ratio helps ensure that the projected image maintains its proportions on the screen. This is important for determining the minimum dimensions of the screen to avoid distortion of the image.
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Related Practice
Textbook Question

Contact lenses are placed right on the eyeball, so the distance from the eye to an object (or image) is the same as the distance from the lens to that object (or image). A certain person can see distant objects well, but his near point is 45.0 cm from his eyes instead of the usual 25.0 cm. Is this person nearsighted or farsighted?

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Textbook Question

Repeat Exercise 34.41 using the same lenses except for the following changes: The second lens is a diverging lens having a focal length of magnitude 60.0 cm.

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Textbook Question

Where is the near point of an eye for which a contact lens with a power of +2.75 diopters is prescribed?

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Textbook Question

A 1.20 cm tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. Find the location and height of the image (call it I1) formed by the lens with a focal length of 40.0 cm.

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Textbook Question

An object is 16.0 cm to the left of a lens. The lens forms an image 36.0 cm to the right of the lens. Draw a principal-ray diagram.

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Textbook Question

Zoom Lens. Consider the simple model of the zoom lens shown in Fig. 34.43a. The converging lens has focal length f1 = 12 cm, and the diverging lens has focal length f2 = -12 cm. The lenses are separated by 4 cm as shown in Fig. 34.43a. (a) For a distant object, where is the of the converging lens? (c) Where is the final image? Compare your answer to Fig. 34.43a.

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