/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 19 A slide projector has a lens of ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 24: Problem 19

A slide projector has a lens of focal length \(12 \mathrm{cm} .\) Each slide is \(24 \mathrm{mm}\) by \(36 \mathrm{mm}\) (see the figure with Problem 16). The projector is used in a room where the screen is \(5.0 \mathrm{m}\) from the projector. How large must the screen be?

Short Answer

Expert verified
Based on the given information, a slide projector with a lens of focal length 12 cm is used to project slides of size 24 mm x 36 mm (2.4 cm x 3.6 cm) onto a screen 5 meters away. Using lens and magnification formulas, the required screen size to accommodate the projected image is approximately 10.94 cm x 16.4 cm.

Step by step solution

01

List the given information

Focal length of the lens (f) = 12 cm Size of each slide (h1) = 24 mm 脳 36 mm = 2.4 cm 脳 3.6 cm Distance between projector and screen (u) = -5 m = -500 cm (note the negative sign, since the object lies on the left side of the lens) We are supposed to find the size of the screen, which will give us the height of the image (h2).
02

Use the lens formula

The lens formula relates the object distance (u), image distance (v), and focal length (f) as follows: 1/f = 1/u + 1/v We need to find the image distance (v). Rearrange the formula to find v: 1/v = 1/f - 1/u Plug in the given values (f and u): 1/v = 1/12 - 1/(-500) Calculate the value of v: 1/v = 1/12 + 1/500 = 629/(12*500) = 629/6000 Now, find the value of v: v = 6000/629 鈮� 9.54 cm
03

Find the magnification (M)

Use the magnification formula to find the magnification (M): M = v/u = -h2/h1 We have the value of v and u. Now, we have to find the size of the image (h2). Rearrange the formula to find h2: h2 = -M * h1 Plug in the values of M and h1: For the vertical size (2.4 cm), h2_vertical = -(9.54/(-500)) * 2.4 鈮� 0.0456 * 2.4 鈮� 0.1094 m 鈮� 10.94 cm For the horizontal size (3.6 cm), h2_horizontal = -(9.54/(-500)) * 3.6 鈮� 0.0456 * 3.6 鈮� 0.164 m 鈮� 16.4 cm
04

Find the size of the screen

So, the size of the screen must be approximately 10.94 cm 脳 16.4 cm to accommodate the projected image.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You plan to project an inverted image \(30.0 \mathrm{cm}\) to the right of an object. You have a diverging lens with focal length \(-4.00 \mathrm{cm}\) located \(6.00 \mathrm{cm}\) to the right of the object. Once you put a second lens at \(18.0 \mathrm{cm}\) to the right of the object, you obtain an image in the proper location. (a) What is the focal length of the second lens? (b) Is this lens converging or diverging? (c) What is the total magnification? (d) If the object is \(12.0 \mathrm{cm}\) high. what is the image height?
You have two lenses of focal length \(25.0 \mathrm{cm}\) (lens 1 ) and $5.0 \mathrm{cm}$ (lens 2 ). (a) To build an astronomical telescope that gives an angular magnification of \(5.0,\) how should you use the lenses (which for objective and which for eyepiece)? Explain. (b) How far apart should they be?

The objective lens of an astronomical telescope forms an image of a distant object at the focal point of the eyepiece, which has a focal length of \(5.0 \mathrm{cm} .\) If the two lenses are \(45.0 \mathrm{cm}\) apart, what is the angular magnification?
Esperanza uses a 35 -mm camera with a standard lens of focal length $50.0 \mathrm{mm}\( to take a photo of her son Carlos, who is \)1.2 \mathrm{m}$ tall and standing \(3.0 \mathrm{m}\) away. (a) What must be the distance between the lens and the film to get a properly focused picture? (b) What is the magnification of the image? (c) What is the height of the image of Carlos on the film?
Suppose that the lens system (cornea + lens) in a particular eye has a focal length that can vary between \(1.85 \mathrm{cm}\) and \(2.00 \mathrm{cm},\) but the distance from the lens system to the retina is only \(1.90 \mathrm{cm} .\) (a) Is this eye nearsighted or farsighted? Explain. (b) What range of distances can the eye see clearly without corrective lenses?
See all solutions

Recommended explanations on Physics Textbooks

Magnetism

Read Explanation

Electromagnetism

Read Explanation

Work Energy and Power

Read Explanation

Waves Physics

Read Explanation

Modern Physics

Read Explanation

Kinematics Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.