Textbook Question
Suppose you are 96 cm from a plane mirror. What area of the mirror is used to reflect the rays entering one eye from a point on the tip of your nose if your pupil diameter is 4.5 mm?
2
views
Ch. 32 - Light: Reflection and Refraction
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. 01 - Introduction, Measurement, Estimating10
- Ch. 02 - Describing Motion: Kinematics in One Dimension30
- Ch. 03 - Kinematics in Two or Three Dimensions; Vectors15
- Ch. 04 - Dynamics: Newton's Laws of Motion16
- Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces22
- Ch. 06 - Gravitation and Newton's Synthesis10
- Ch. 07 - Work and Energy21
- Ch. 08 - Conservation of Energy33
- Ch. 09 - Linear Momentum26
- Ch. 10 - Rotational Motion41
- Ch. 11 - Angular Momentum; General Rotation27
- Ch. 12 - Static Equilibrium; Elasticity and Fracture27
- Ch. 13 - Fluids28
- Ch. 14 - Oscillations14
- Ch. 15 - Wave Motion35
- Ch. 16 - Sound5
- Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law40
- Ch. 18 - Kinetic Theory of Gases18
- Ch. 19 - Heat and the First Law of Thermodynamics31
- Ch. 20 - Second Law of Thermodynamics32
- Ch. 21 - Electric Charge and Electric Field7
- Ch. 23 - Electric Potential20
- Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage15
- Ch. 25 - Electric Current and Resistance32
- Ch. 26 - DC Circuits22
- Ch. 27 - Magnetism21
- Ch. 28 - Sources of Magnetic Field24
- Ch. 29 - Electromagnetic Induction and Faraday's Law21
- Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits42
- Ch. 31 - Maxwell's Equations and Electromagnetic Waves25
- Ch. 32 - Light: Reflection and Refraction42
- Ch. 33 - Lenses and Optical Instruments21
- Ch. 34 - The Wave Nature of Light: Interference and Polarization26
- Ch. 35 - Diffraction24
- Ch. 36 - The Special Theory of Relativity29
- Ch. 38 - Quantum Mechanics1
- Ch. 40 - Molecules and Solids6
- Ch. 43 - Elementary Particles3
- Ch. 44 - Astrophysics and Cosmology9
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
Chapter 31, Problem 16
A dentist wants a small mirror that, when 2.00 cm from a tooth, will produce a 3.0 x upright image. What kind of mirror must be used and what must its radius of curvature be?
Verified step by step guidance1
Determine the type of mirror: Since the image is upright and magnified, the mirror must be a concave mirror. Concave mirrors can produce upright, magnified images when the object is within the focal length of the mirror.
Use the magnification formula to relate the image distance \(d_i\) and object distance \(d_o\): \(M = \frac{d_i}{d_o}\), where \(M\) is the magnification. Substitute \(M = 3.0\) and \(d_o = 2.00\,\text{cm}\) to solve for \(d_i\).
Apply the mirror equation to find the focal length \(f\): \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\). Use the values of \(d_o\) and \(d_i\) from the previous step to calculate \(f\).
Relate the focal length \(f\) to the radius of curvature \(R\): \(R = 2f\). Use the focal length obtained in the previous step to find the radius of curvature.
Summarize the results: The mirror is a concave mirror, and its radius of curvature can be determined using the steps above.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Types of Mirrors
There are two main types of mirrors: concave and convex. Concave mirrors can produce real and inverted images or virtual and upright images, depending on the object's distance from the mirror. In contrast, convex mirrors always produce virtual, upright images. For the scenario described, a concave mirror is required to achieve the specified upright image at a given distance.
Recommended video:
09:03
Mirror Equation
Mirror Formula
The mirror formula relates the object distance (u), image distance (v), and focal length (f) of a mirror: 1/f = 1/v + 1/u. This formula is essential for determining the characteristics of the image produced by the mirror. In this case, knowing the object distance and the magnification allows us to find the image distance and subsequently the focal length.
Recommended video:
09:03Mirror Equation
Magnification
Magnification (M) is the ratio of the height of the image (h') to the height of the object (h), and it can also be expressed in terms of distances: M = -v/u. A positive magnification indicates an upright image, while a negative value indicates an inverted image. In this problem, the magnification of 3.0 signifies that the image is upright and larger than the object, which is a key factor in determining the type of mirror and its properties.
Recommended video:
09:03Mirror Equation
Related Practice
Textbook Question
The lateral magnification of a convex mirror is +0.75 for objects 3.2 m from the mirror. What is the focal length of this mirror?
1
views
Textbook Question
An object 4.0 mm high is placed 18 cm from a convex mirror of radius of curvature 18 cm. Compute the image size, using Eq. 32–3.
1
views
Textbook Question
An object 4.0 mm high is placed 18 cm from a convex mirror of radius of curvature 18 cm. Show that the (negative) image distance can be computed from Eq. 32–2 using a focal length of -9.0 cm.
1
views
Textbook Question
You look at yourself in a shiny 8.4-cm-diameter Christmas tree ball. If your face is 25.0 cm away from the ball’s front surface, where is your image? Is it real or virtual? Is it upright or inverted?
1
views
Textbook Question
An object 4.0 mm high is placed 18 cm from a convex mirror of radius of curvature 18 cm. Show by ray tracing that the image is virtual, and estimate the image distance.
1
views