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 14
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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Determine the radius of curvature (R) of the spherical mirror. Since the diameter of the ball is 8.4 cm, the radius is half of that: R = 8.4 cm / 2 = 4.2 cm. The focal length (f) of a spherical mirror is related to the radius of curvature by the formula: . Substitute R = 4.2 cm to find f.
Identify the type of mirror. A shiny Christmas tree ball is a convex mirror because the reflective surface is on the outside of the sphere. For convex mirrors, the focal length (f) is negative. Use the value of f calculated in the previous step, but assign it a negative sign.
Use the mirror equation to find the image distance (di): , where do is the object distance (25.0 cm), f is the focal length, and di is the image distance. Rearrange the equation to solve for di: .
Substitute the known values of f (negative) and do (25.0 cm) into the rearranged mirror equation. Perform the subtraction to find the reciprocal of di, then take the reciprocal of that result to find di. Remember that for convex mirrors, the image distance will always be positive, indicating that the image is virtual.
Analyze the nature of the image. For convex mirrors, the image is always virtual (it cannot be projected onto a screen), upright (not inverted), and smaller than the object. Confirm these characteristics based on the calculated image distance and the properties of convex mirrors.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Concave Mirrors
The shiny surface of the Christmas tree ball acts like a concave mirror, which can form images based on the position of the object relative to its focal point. Concave mirrors can produce both real and virtual images depending on the object's distance from the mirror's surface.
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Ray Diagrams for Concave Mirrors
Image Formation
The formation of an image by a mirror involves the principles of reflection and the mirror equation. The distance of the object from the mirror and the radius of curvature determine where the image is formed, whether it is real or virtual, and its orientation (upright or inverted).
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05:51Refraction at Spherical Surfaces
Mirror Equation and Magnification
The mirror equation (1/f = 1/do + 1/di) relates the focal length (f), object distance (do), and image distance (di). Magnification (m) indicates the size and orientation of the image, calculated as m = -di/do. A positive magnification indicates an upright image, while a negative value indicates an inverted image.
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09:03Mirror Equation
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
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?
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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 that the (negative) image distance can be computed from Eq. 32–2 using a focal length of -9.0 cm.
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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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