Textbook Question
A 1.0-cm-tall object is 10 cm in front of a converging lens that has a 30 cm focal length. Calculate the image position and height. Compare with your ray-tracing answers in part a.
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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 28
Find the focal length of the glass lens in FIGURE EX34.28.
Verified step by step guidance1
Step 1: Identify the type of lens shown in the figure. The lens in the image is a diverging lens, as it causes parallel rays to spread out and appear to originate from a focal point on the same side as the incoming light.
Step 2: Recall the lens formula: \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \), where \( f \) is the focal length, \( d_o \) is the object distance, and \( d_i \) is the image distance. For a diverging lens, the focal length \( f \) is negative.
Step 3: From the figure, observe that the object distance \( d_o \) is 40 cm and the image distance \( d_i \) is also 40 cm. Note that for a diverging lens, the image distance \( d_i \) is negative because the image is virtual and on the same side as the object.
Step 4: Substitute the values into the lens formula: \( \frac{1}{f} = \frac{1}{40} + \frac{1}{-40} \). Simplify the equation to find \( \frac{1}{f} \).
Step 5: Solve for \( f \) by taking the reciprocal of \( \frac{1}{f} \). The result will give the focal length of the lens, which will be negative, indicating a diverging lens.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Focal Length
The focal length of a lens is the distance from the lens to the focal point, where parallel rays of light converge or appear to diverge. It is a crucial parameter in lens optics, determining how strongly the lens converges or diverges light. The focal length can be positive for converging lenses and negative for diverging lenses.
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Lens Maker's Equation
The Lens Maker's Equation relates the focal length of a lens to the radii of curvature of its two surfaces and the refractive index of the lens material. It is expressed as 1/f = (n - 1) * (1/R1 - 1/R2), where f is the focal length, n is the refractive index, and R1 and R2 are the radii of curvature of the lens surfaces. This equation is essential for calculating the focal length based on the lens geometry.
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Ray Diagrams
Ray diagrams are graphical representations used to illustrate how light rays interact with lenses. They help visualize the paths of light as they pass through the lens, showing how they converge or diverge. By drawing the principal rays, such as the parallel ray, the focal ray, and the central ray, one can determine the image location and characteristics, which are vital for understanding lens behavior.
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Related Practice
Textbook Question
An object is 20 cm in front of a converging lens with a focal length of 10 cm. Use ray tracing to determine the location of the image. Is the upright or inverted?
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Textbook Question
Find the focal length of the plano-concave polystyrene plastic lens in FIGURE EX34.25.
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Textbook Question
A goldfish lives in a 50-cm-diameter spherical fish bowl. The fish sees a cat watching it. If the cat's face is 20 cm from the edge of the bowl, how far from the edge does the fish see it as being? (You can ignore the thin glass wall of the bowl.)
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Textbook Question
A giant ocean tank at an aquarium has acrylic plastic walls 18 cm thick. The index of refraction of acrylic plastic is 1.49. A fish is 220 cm from the inside wall. To a viewer on the outside, how far does the fish appear to be from the outside wall? Hint: The of the first refraction is the object for the second refraction.
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Textbook Question
A 1.0-cm-tall candle flame is 60 cm from a lens with a focal length of 20 cm. What are the distance and the height of the flame's image?
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