Textbook Question
CALC A converging lens with focal length f creates a real image of an object. What is the minimum possible distance between the object and its image? Your answer will be a multiple of f.
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Ch 34: Ray Optics
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 34, Problem 68
A lightbulb is 3.0 m from a wall. What are the focal length and the position (measured from the bulb) of a lens that will form an on the wall that is twice the size of the lightbulb?
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Identify the given information: The object distance \( d_o \) is 3.0 m, the image distance \( d_i \) is unknown, and the magnification \( M \) is given as 2 (since the image is twice the size of the object).
Use the magnification formula \( M = -\frac{d_i}{d_o} \) to relate the image distance \( d_i \) to the object distance \( d_o \). Substitute \( M = 2 \) and \( d_o = 3.0 \) m into the equation to solve for \( d_i \).
Once \( d_i \) is determined, use the lens equation \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \) to calculate the focal length \( f \). Substitute the values of \( d_o \) and \( d_i \) into the equation.
Rearrange the lens equation to isolate \( f \): \( f = \frac{1}{\frac{1}{d_o} + \frac{1}{d_i}} \). Perform the necessary algebraic manipulations to simplify the expression for \( f \).
Verify the results by checking that the calculated focal length and image distance satisfy both the lens equation and the magnification condition. Ensure the units are consistent throughout the calculations.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Lens Formula
The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens through the equation 1/f = 1/v - 1/u. This formula is essential for determining how a lens will manipulate light to form images at specific distances, which is crucial for solving the problem of image formation on the wall.
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Lens Maker Equation
Magnification
Magnification (M) is the ratio of the height of the image (h') to the height of the object (h), expressed as M = h'/h. In this scenario, the problem states that the image formed on the wall is twice the size of the lightbulb, indicating a magnification of 2. Understanding magnification helps in determining the relationship between the object and image distances.
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09:03Mirror Equation
Sign Convention in Optics
In optics, the sign convention dictates how distances are measured in relation to the lens. Typically, distances measured in the direction of the incoming light are negative, while those in the direction of outgoing light are positive. This convention is crucial for correctly applying the lens formula and calculating the focal length and image position.
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Guided course
08:55Net Torque & Sign of Torque
Related Practice
Textbook Question
A 25-cm-long rod lies along the optical axis of a converging lens, perpendicular to the lens plane. The lens has a 30 cm focal length. The rod's real , along the optical axis on the other side of the lens, is also 25 cm long. What is the distance from the lens to the nearest end of the rod?
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Textbook Question
An old-fashioned slide projector needs to create a 98-cm-high of a 2.0-cm-tall slide. The screen is 300 cm from the slide. What focal length does the lens need? Assume that it is a thin lens.
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Textbook Question
A plano-concave glass lens (flat on one side, concave on the other) creates an with magnification +0.40 of an object 75 cm from the lens. What is the radius of curvature of the lens's curved surface?
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Textbook Question
An object is 60 cm from a screen. What are the radii of a symmetric converging plastic lens (i.e., two equally curved surfaces) that will form an image on the screen twice the height of the object?
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Textbook Question
A 2.0-cm-tall candle flame is 2.0 m from a wall. You happen to have a lens with a focal length of 32 cm. How many places can you put the lens to form a well-focused image of the candle flame on the wall? For each location, what are the height and orientation of the image?
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