Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 23: Problem 52

A concave mirror has a radius of curvature of \(5.0 \mathrm{m} .\) An object, initially \(2.0 \mathrm{m}\) in front of the mirror, is moved back until it is \(6.0 \mathrm{m}\) from the mirror. Describe how the image location changes.

Short Answer

Expert verified
Answer: As the object moves from 2.0m to 6.0m in front of the concave mirror, the image location moves closer to the mirror, from 5.0m to 3.75m.

Step by step solution

01

Since we are given the radius of curvature \(R\), we can find the focal length \(f\) using the following formula: \(f = \frac{R}{2}\) where: - \(R=5.0\,m\) (radius of curvature) Now let's calculate the focal length: \(f = \frac{5.0}{2} = 2.5\,m\) #Step 2: Calculate the initial image distance#

To find the initial image distance \(d_{i1}\), we use the mirror equation with the given initial object distance \(d_\text{o1}=2.0\,m\). Plugging the values into the equation: \(\frac{1}{2.5}=\frac{1}{2.0}+\frac{1}{d_{i1}}\) Solving for \(d_{i1}\), we get: \(d_{i1} = \frac{1}{\frac{1}{2.5}-\frac{1}{2}} = 5.0\,m\) #Step 3: Calculate the final image distance#
02

Similarly, for the final image distance \(d_{i2}\), we use the mirror equation with the given final object distance \(d_\text{o2}=6.0\,m\): \(\frac{1}{2.5}=\frac{1}{6.0}+\frac{1}{d_{i2}}\) Solving for \(d_{i2}\), we get: \(d_{i2} = \frac{1}{\frac{1}{2.5}-\frac{1}{6}} = 3.75\,m\) #Step 4: Describe how the image location changes#

The initial image distance was \(5.0\,m\), and the final image distance is \(3.75\,m\). Thus, as the object moves from \(2.0\,m\) to \(6.0\,m\) in front of the concave mirror, the image location moves closer to the mirror, from \(5.0\,m\) to \(3.75\,m\).

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

An object that is \(6.00 \mathrm{cm}\) tall is placed \(40.0 \mathrm{cm}\) in front of a diverging lens. The magnitude of the focal length of the lens is \(20.0 \mathrm{cm} .\) Find the image position and size. Is the image real or virtual? Upright or inverted?
Show that the deviation angle \(\delta\) for a ray striking a thin converging lens at a distance \(d\) from the principal axis is given by \(\delta=d l f .\) Therefore, a ray is bent through an angle \(\delta\) that is proportional to \(d\) and does not depend on the angle of the incident ray (as long as it is paraxial). [Hint: Look at the figure and use the small-angle approximation \(\sin \theta=\tan \theta \approx \theta(\text { in radians) } .]\)
A manufacturer is designing a shaving mirror, which is intended to be held close to the face. If the manufacturer wants the image formed to be upright and as large as possible, what characteristics should he choose? (type of mirror? long or short focal length relative to the object distance of face to mirror?)
A beam of light in air is incident on a stack of four flat transparent materials with indices of refraction 1.20 \(1.40,1.32,\) and \(1.28 .\) If the angle of incidence for the beam on the first of the four materials is \(60.0^{\circ},\) what angle does the beam make with the normal when it emerges into the air after passing through the entire stack?
(a) Sunlight reflected from the still surface of a lake is totally polarized when the incident light is at what angle with respect to the horizontal? (b) In what direction is the reflected light polarized? (c) Is any light incident at this angle transmitted into the water? If so, at what angle below the horizontal does the transmitted light travel?
See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Scientific Method Physics

Read Explanation

Radiation

Read Explanation

Modern Physics

Read Explanation

Magnetism

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