Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 24: Problem 30

(a) What is the focal length of a magnifying glass that gives an angular magnification of 8.0 when the image is at infinity? (b) How far must the object be from the lens? Assume the lens is held close to the eye.

Short Answer

Expert verified
Answer: The focal length of the magnifying glass is approximately 3.57 cm, and the object should be placed at a distance of approximately 1.39 cm from the lens.

Step by step solution

01

Write the formula for angular magnification and lens formula

The formula for angular magnification (M) of a magnifying glass when the image is at infinity is given by: M = 1 + (D / f) where, M = Angular magnification D = The distance of the nearest clear vision (25 cm) f = Focal length of the lens The lens formula is given by: 1 / f = 1 / u + 1 / v where, f = Focal length of the lens u = Object distance from the lens v = Image distance from the lens (a) We need to find the focal length (f) when angular magnification (M) is 8.0. (b) After finding the focal length, we will find the object distance (u) by using the lens formula.
02

Solve the angular magnification formula for the focal length (f)

Rearrange the formula for angular magnification to find the value of focal length (f): f = D / (M - 1) Now substitute the given values: M = 8.0 D = 25 cm f = 25 / (8 - 1) f = 25 / 7 f = 3.57 cm So, the focal length of the magnifying glass is 3.57 cm.
03

Use the lens formula to find the object distance (u)

When the image is at infinity, the image distance (v) is considered to be infinite. The lens formula will become: 1 / f = 1 / u Now, rearrange the formula to find the value of the object distance (u): u = f / (1 - f) Substitute the value of the focal length (f = 3.57 cm): u = 3.57 / (1 - 3.57) u = 3.57 / -2.57 u = -1.39 cm Since the distance cannot be negative, we'll take the absolute value of the result: u = 1.39 cm So, the object must be 1.39 cm away from the lens.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Jordan is building a compound microscope using an eyepiece with a focal length of \(7.50 \mathrm{cm}\) and an objective with a focal length of $1.500 \mathrm{cm} .\( He will place the specimen a distance of \)1.600 \mathrm{cm}$ from the objective. (a) How far apart should Jordan place the lenses? (b) What will be the angular magnification of this microscope?
A statue is \(6.6 \mathrm{m}\) from the opening of a pinhole camera, and the screen is \(2.8 \mathrm{m}\) from the pinhole. (a) Is the image erect or inverted? (b) What is the magnification of the image? (c) To get a brighter image, we enlarge the pinhole to let more light through, but then the image looks blurry. Why? (d) To admit more light and still have a sharp image, we replace the pinhole with a lens. Should it be a converging or diverging lens? Why? (e) What should the focal length of the lens be?
An object is located at \(x=0 .\) At \(x=2.50 \mathrm{cm}\) is a converging lens with a focal length of \(2.00 \mathrm{cm},\) at \(x=16.5 \mathrm{cm}\) is an unknown lens, and at \(x=19.8 \mathrm{cm}\) is another converging lens with focal length \(4.00 \mathrm{cm} .\) An upright image is formed at $x=39.8 \mathrm{cm} .$ For each lens, the object distance exceeds the focal length. The magnification of the system is \(6.84 .\) (a) Is the unknown lens diverging or converging? (b) What is the focal length of the unknown lens? (c) Draw a ray diagram to confirm your answer.
The wing of an insect is \(1.0 \mathrm{mm}\) long. When viewed through a microscope, the image is \(1.0 \mathrm{m}\) long and is located \(5.0 \mathrm{m}\) away. Determine the angular magnification.
Comprehensive Problems Good lenses used in cameras and other optical devices are actually compound lenses, made of five or more lenses put together to minimize distortions, including chromatic aberration. Suppose a converging lens with a focal length of \(4.00 \mathrm{cm}\) is placed right next to a diverging lens with focal length of \(-20.0 \mathrm{cm} .\) An object is placed \(2.50 \mathrm{m}\) to the left of this combination. (a) Where will the image be located? (b) Is the image real or virtual?
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Mechanics and Materials

Read Explanation

Waves Physics

Read Explanation

Work Energy and Power

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Modern 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.

Sign-up for free