Textbook Question
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?
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Ch. 32 - Light: Reflection and Refraction
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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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 12
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?
Verified step by step guidance1
Start by recalling the formula for lateral magnification \( M \) in a mirror: \( M = -\frac{q}{p} \), where \( q \) is the image distance and \( p \) is the object distance. Here, \( M = +0.75 \) and \( p = 3.2 \ \text{m} \).
Rearrange the magnification formula to solve for \( q \): \( q = -M \cdot p \). Substitute the given values of \( M \) and \( p \) into the equation to find \( q \).
Next, use the mirror equation: \( \frac{1}{f} = \frac{1}{p} + \frac{1}{q} \), where \( f \) is the focal length, \( p \) is the object distance, and \( q \) is the image distance. Substitute the known values of \( p \) and \( q \) into this equation.
Simplify the terms \( \frac{1}{p} \) and \( \frac{1}{q} \) to calculate \( \frac{1}{f} \).
Finally, take the reciprocal of \( \frac{1}{f} \) to find the focal length \( f \) of the convex mirror.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Lateral Magnification
Lateral magnification (m) is the ratio of the height of the image (h') to the height of the object (h). For mirrors, it can also be expressed in terms of the object distance (u) and the image distance (v) as m = -v/u. A positive magnification indicates that the image is upright relative to the object, which is typical for virtual images produced by convex mirrors.
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Mirror Equation
Convex Mirror Properties
Convex mirrors are curved outward and always produce virtual, upright, and reduced images. The focal length (f) of a convex mirror is considered positive, and it is located behind the mirror. The mirror formula, 1/f = 1/v + 1/u, relates the focal length to the object and image distances, allowing for calculations involving image formation.
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Mirror Formula
The mirror formula is a fundamental equation in optics that relates the object distance (u), image distance (v), and focal length (f) of a mirror. It is expressed as 1/f = 1/v + 1/u. This formula is essential for solving problems involving mirrors, as it allows for the determination of unknown distances when the other parameters are known.
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Related Practice
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?
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Textbook Question
Suppose that you want to take a photograph of yourself as you look at your image in a mirror 2.4 m away. For what distance should the camera lens be focused?
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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?
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Textbook Question
A person whose eyes are 1.64 m above the floor stands 2.60 m in front of a vertical plane mirror whose bottom edge is 38 cm above the floor, Fig. 32–48. What is the horizontal distance x, from the base of the wall supporting the mirror to the nearest point on the floor that can be seen reflected in the mirror?
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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.
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