/*! 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 4 If you run away from a plane mir... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 24: Problem 4

If you run away from a plane mirror at \(2.40 \mathrm{~m} / \mathrm{s},\) at what speed does your image move away from you?

Short Answer

Expert verified
The image moves away at 4.80 m/s.

Step by step solution

01

Understanding the Concept

When you move away from a plane mirror, your image moves with respect to both you and the mirror. Due to the symmetry of reflection, the distance between you and your image doubles your movement speed.
02

Calculating the Speed of the Image

Since you run away from the mirror at a speed of \(2.40 \, \text{m/s}\), your image moves away from the mirror at the same speed but in the opposite direction. This results in your image moving away from you at twice your running speed.
03

Final Calculation

The speed at which the image moves away from you is calculated as twice your speed, \(2.40 \, \text{m/s} \times 2 = 4.80 \, \text{m/s}\).

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Plane Mirror Reflections
In the realm of optics, a plane mirror is a flat reflective surface that bounces back light according to the law of reflection. This law states that the angle of incidence equals the angle of reflection. When light strikes the mirror, it forms an image with characteristics distinctly different from those in concave or convex mirrors.
  • The image formed is virtual, meaning it cannot be projected onto a screen.
  • The image is the same size as the object. It is also upright, maintaining the same orientation as the object.
  • The distance between the object and the mirror is equal to the distance between the image and the mirror.
Understanding these properties helps us deduce the behavior of images in plane mirrors, such as those faced in problems involving motion related to a mirror.
Relative Motion
Relative motion examines the movement of one object as observed from another moving object. It plays a key role in understanding the interaction between you and your mirrored image.
  • In a plane mirror, as you move away from it, your image behaves as if it is on the opposite side of the mirror, mimicking your actions.
  • The concept of relative motion helps us deduce that if you move away from the plane mirror, the image also seems to move away from you.
This is due to how the image replicates your motion, albeit in a mirrored path. It's basically a dance of imitation, governed by the simple principles of relative movement within the confines of rigid reflection rules.
Speed Calculation
Speed calculation in the context of mirror reflections involves understanding that the image effectively doubles the speed of your movement relative to your position. For instance, if you move at a certain speed from a mirror, your image theoretically does the same, moving away from the mirror.
  • Thus, it maintains the same pace but appears as if it's on a mirrored path, which creates an additive effect when considering your relative movement.
  • The key point is that if you are moving at a speed of \( 2.40 \, \text{m/s} \) away from a mirror, your image's speed away from you will actually be \( 4.80 \, \text{m/s} \).
This doubling is because the image replicates your movement, only in a perceived reverse direction from the perspective of relative motion.
Reflection Symmetry
Reflection symmetry, also known as mirror symmetry, is the concept where one half of an object is a mirror image of the other half. It is a principle deeply embedded in plane mirror reflections. Whenever you stand in front of a plane mirror, you witness reflection symmetry firsthand.
  • The reflection is created by the identical and opposite path of the light rays, giving you a mirror image that appears to have the same size, shape, and distance as you, but flipped across the mirror's surface.
  • This symmetry means that movements are mirrored precisely, which is why your mirrored image moves with you at twice your speed when you walk away from the mirror.
Understanding reflection symmetry helps clarify why mirrored images behave the way they do when objects, like you, move in front of a plane mirror.

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

The cornea of the eye has a radius of curvature of approximately \(0.50 \mathrm{~cm},\) and the aqueous humor behind it has an index of refraction of \(1.35 .\) The thickness of the cornea itself is small enough that we can ignore it. The depth of a typical human eye is around \(25 \mathrm{~mm}\). (a) What would have to be the radius of curvature of the cornea so that it alone would focus the image of a distant mountain on the retina, which is at the back of the eye opposite the cornea? (b) If the cornea focused the mountain correctly on the retina as described in part (a), would it also focus the text from a computer screen on the retina if that screen were \(25 \mathrm{~cm}\) in front of the eye? If not, where would it focus that text, in front of or behind the retina? (c) Given that the cornea has a radius of curvature of about \(5.0 \mathrm{~mm},\) where does it actually focus the mountain? Is this in front of or behind the retina? Does this help you see why the eye needs help from a lens to complete the task of focusing?

The diameter of Mars is \(6794 \mathrm{~km}\), and its minimum distance from the earth is \(5.58 \times 10^{7} \mathrm{~km} .\) (a) When Mars is at this distance, find the diameter of the image of Mars formed by a spherical, concave telescope mirror with a focal length of \(1.75 \mathrm{~m}\). (b) Where is the image located?

A converging lens has a focal length of \(14.0 \mathrm{~cm} .\) For each of two objects located to the left of the lens, one at a distance of \(18.0 \mathrm{~cm}\) and the other at a distance of \(7.00 \mathrm{~cm},\) determine (a) the image position, (b) the magnification, (c) whether the image is real or virtual, and (d) whether the image is upright or inverted. Draw a principal-ray diagram in each case.

A coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of \(18.0 \mathrm{~cm}\). An image of the \(1.5-\mathrm{cm}\) -tall coin is formed \(6.00 \mathrm{~cm}\) behind the glass shell. Where is the coin located? Determine the size, orientation, and nature (real or virtual) of the image.

A spherical, concave shaving mirror has a radius of curvature of \(32.0 \mathrm{~cm} .\) (a) What is the magnification of a person's face when it is \(12.0 \mathrm{~cm}\) to the left of the vertex of the mirror? (b) Where is the image? Is the image real or virtual? (c) Draw a principal-ray diagram showing the formation of the image.
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Classical Mechanics

Read Explanation

Turning Points in Physics

Read Explanation

Energy Physics

Read Explanation

Force

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.