Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 33: Problem 87

You visit your eye doctor and discover that you require lenses having a diopter value of -8.4 . Are you nearsighted or farsighted? With uncorrected vision, how far away from your eyes must you hold a book to read clearly?

Short Answer

Expert verified
Answer: A person with a diopter value of -8.4 is nearsighted. To read a book clearly without correction, they should hold it approximately 11.9 centimeters away from their eyes.

Step by step solution

01

Determine if the person is nearsighted or farsighted

A diopter is a unit of measurement for the optical power of a lens. A positive diopter value indicates farsightedness (difficulty in seeing things close-up), while a negative diopter value indicates nearsightedness (difficulty in seeing things far away). Since the given diopter value is -8.4, the person is nearsighted.
02

Calculate the focal length

To determine the comfortable reading distance for the person, we will use the formula for the focal length (f) of a lens: f = 1 / D where D is the diopter value. In this case, D = -8.4, so: f = 1 / (-8.4) = -0.119 meters, or -11.9 centimeters Since the focal length is negative, it indicates that the focal point is on the same side of the lens as the object being viewed. This is a characteristic of a diverging lens, which is used to correct nearsightedness.
03

Determine the distance to hold the book

The comfortable reading distance is determined by the focal point of the uncorrected vision. As the focal length is -11.9 centimeters, the person must hold the book at approximately 11.9 centimeters away from their eyes to read it clearly without correction.

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

A camera has a lens with a focal length of \(60 . \mathrm{mm} .\) Suppose you replace the normal lens with a zoom lens whose focal length can be varied from \(35 . \mathrm{mm}\) to \(250 . \mathrm{mm}\) and use the camera to photograph an object at infinity. Compared to a 60.-mm lens, what magnification of the image would be achieved using the \(240 .-\mathrm{mm}\) focal length?

Two refracting telescopes are used to look at craters on the Moon. The objective focal length of both telescopes is \(95.0 \mathrm{~cm}\) and the eyepiece focal length of both telescopes is \(3.80 \mathrm{~cm} .\) The telescopes are identical except for the diameter of the lenses. Telescope A has an objective diameter of \(10.0 \mathrm{~cm}\) while the lenses of telescope \(\mathrm{B}\) are scaled up by a factor of two, so that its objective diameter is \(20.0 \mathrm{~cm}\). a) What are the angular magnifications of telescopes \(A\) and \(B\) ? b) Do the images produced by the telescopes have the same brightness? If not, which is brighter and by how much?

A telescope is advertised as providing a magnification of magnitude 41 using an eyepiece of focal length \(4.0 \cdot 10^{1} \mathrm{~mm}\). What is the focal length of the objective?

For a person whose near point is \(115 \mathrm{~cm},\) so that he can read a computer monitor at \(55 \mathrm{~cm},\) what power of read ing glasses should his optician prescribe, keeping the lenseye distance of \(2.0 \mathrm{~cm}\) for his spectacles?

Mirrors for astronomical instruments are invariably first-surface mirrors: The reflective coating is applied on the surface exposed to the incoming light. Household mirrors, on the other hand, are second-surface mirrors: The coating is applied to the back of the glass or plastic material of the mirror. (You can tell the difference by bringing the tip of an object close to the surface of the mirror. Object and image will nearly touch with a first-surface mirror; a gap will remain between them with a second-surface mirror.) Explain the reasons for these design differences.
See all solutions

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Read Explanation

Magnetism

Read Explanation

Circular Motion and Gravitation

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Physics of Motion

Read Explanation

Waves 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