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 36a
A 1.0-cm-tall object is 60 cm in front of a diverging lens that has a −30 cm focal length. Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.
Verified step by step guidance1
Start by understanding the problem: A diverging lens has a negative focal length (f = -30 cm). The object is placed 60 cm in front of the lens, and its height is 1.0 cm. We need to determine the image distance and image height using ray tracing.
Draw a scaled diagram: On graph paper, draw the principal axis (a horizontal line). Mark the optical center of the lens at the origin. Place the object 60 cm to the left of the lens on the principal axis, and draw the object as a vertical arrow 1.0 cm tall.
Trace the first ray: Draw a ray from the top of the object parallel to the principal axis. After passing through the lens, this ray will diverge as if it came from the focal point on the same side as the object. Extend the diverging ray backward with a dashed line to locate its virtual origin.
Trace the second ray: Draw a ray from the top of the object heading toward the focal point on the opposite side of the lens. After passing through the lens, this ray will emerge parallel to the principal axis. Extend this ray backward with a dashed line to locate its virtual origin.
Locate the image: The point where the two dashed lines intersect is the location of the virtual image. Measure the distance from the lens to this point to find the image distance (denoted as \(d_i\)). Measure the height of the image on the diagram to determine the image height. Note that the image will be upright and smaller than the object.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Diverging Lens
A diverging lens, also known as a concave lens, causes parallel rays of light to spread out or diverge. It has a negative focal length, which means that the focal point is virtual and located on the same side as the incoming light. This type of lens always produces virtual images that are upright and smaller than the object.
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Thin Lens Equation
Ray Tracing
Ray tracing is a graphical method used to determine the position and characteristics of an image formed by a lens. By drawing specific rays from the object through the lens, one can locate the image's position. The principal rays typically used include the parallel ray, which passes through the focal point after refraction, and the focal ray, which travels through the center of the lens without bending.
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Image Distance and Height
Image distance refers to the distance from the lens to the image formed, while image height is the size of the image compared to the object. For a diverging lens, the image distance is negative, indicating that the image is virtual and located on the same side as the object. The magnification, which relates the image height to the object height, can be calculated using the formula: magnification = image height / object height = - image distance / object distance.
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Related Practice
Textbook Question
An object is 12 cm in front of a concave mirror with a focal length of 20 cm. Use ray tracing to locate the image. Is the image upright or inverted?
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Textbook Question
A 2.0-cm-tall object is 15 cm in front of a plano-convex polystyrene plastic lens that has a 13 cm radius of curvature. What are the (a) position and (b) height of the image?
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Textbook Question
An advanced computer sends information to its various parts via infrared light pulses traveling through silicon fibers. To acquire data from memory, the central processing unit sends a light-pulse request to the memory unit. The memory unit processes the request, then sends a data pulse back to the central processing unit. The memory unit takes 0.5 ns to process a request. If the information has to be obtained from memory in 2.0 ns, what is the maximum distance the memory unit can be from the central processing unit?
Textbook Question
A laser beam in air is incident on a liquid at an angle of 53° with respect to the normal. The laser beam's angle in the liquid is 35°. What is the liquid's index of refraction?
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Textbook Question
A red ball is placed at point A in FIGURE P34.44. What are the (x, y) coordinates of each image?
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