Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 24: Problem 26

The distance from the lens system (cornea + lens) of a particular eye to the retina is \(1.75 \mathrm{cm} .\) What is the focal length of the lens system when the eye produces a clear image of an object \(25.0 \mathrm{cm}\) away?

Short Answer

Expert verified
Answer: The focal length is approximately \(1.636 \mathrm{cm}\).

Step by step solution

01

Understand the Lens Formula

Using the lens formula, we can determine the focal length of the lens system. The formula is: \[\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}\] where: - \(f\) is the focal length of the lens system, - \(d_o\) is the distance from the object to the lens system, and - \(d_i\) is the distance from the lens system to the image (or the distance from the lens system to the retina). Given that the image is formed exactly on the retina, we can use the distance from the lens system to the retina as \(d_i\).
02

Substitute the given values

We know that the distance from the object to the eye (\(d_o\)) is \(25.0 \mathrm{cm}\), and the distance from the lens system to the retina (\(d_i\)) is \(1.75 \mathrm{cm}\). Substitute these values into the lens formula: \[\frac{1}{f} = \frac{1}{25.0 \mathrm{cm}} + \frac{1}{1.75 \mathrm{cm}}\]
03

Calculate the focal length

To find the focal length \(f\), first compute the sum of the fractions and then find the inverse: \[\frac{1}{f} = 0.04 \mathrm{cm^{-1}}+0.5714 \mathrm{cm^{-1}}\] \[\frac{1}{f} = 0.6114 \mathrm{cm^{-1}}\] \[f = \frac{1}{0.6114 \mathrm{cm^{-1}}}\]
04

Find the final answer

Calculate the focal length of the lens system: \[f \approx 1.636 \mathrm{cm}\] The focal length of the lens system when the eye produces a clear image of an object \(25.0 \mathrm{cm}\) away is approximately \(1.636 \mathrm{cm}\).

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 nearsighted man cannot clearly see objects more than \(2.0 \mathrm{m}\) away. The distance from the lens of the eye to the retina is \(2.0 \mathrm{cm},\) and the eye's power of accommodation is \(4.0 \mathrm{D}\) (the focal length of the cornea-lens system increases by a maximum of \(4.0 \mathrm{D}\) over its relaxed focal length when accommodating for nearby objects). (a) As an amateur optometrist, what corrective eyeglass lenses would you prescribe to enable him to clearly see distant objects? Assume the corrective lenses are $2.0 \mathrm{cm}$ from the eyes. (b) Find the nearest object he can see clearly with and without his glasses.
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?
A convex lens of power +12 D is used as a magnifier to examine a wildflower. What is the angular magnification if the final image is at (a) infinity or (b) the near point of \(25 \mathrm{cm} ?\)
A microscope has an eyepiece of focal length \(2.00 \mathrm{cm}\) and an objective of focal length \(3.00 \mathrm{cm} .\) The eyepiece produces a virtual image at the viewer's near point \((25.0 \mathrm{cm}\) from the eye). (a) How far from the eyepiece is the image formed by the objective? (b) If the lenses are \(20.0 \mathrm{cm}\) apart, what is the distance from the objective lens to the object being viewed? (c) What is the angular magnification?
A man requires reading glasses with \(+2.0 \mathrm{D}\) power to read a book held \(40.0 \mathrm{cm}\) away with a relaxed eye. Assume the glasses are $2.0 \mathrm{cm}$ from his eyes. (a) What is his uncorrected far point? (b) What refractive power lenses should he use for distance vision? (c) His uncorrected near point is \(1.0 \mathrm{m} .\) What should the refractive powers of the two lenses in his bifocals be to give him clear vision from \(25 \mathrm{cm}\) to infinity?
See all solutions

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Read Explanation

Force

Read Explanation

Wave Optics

Read Explanation

Electrostatics

Read Explanation

Quantum Physics

Read Explanation

Measurements

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