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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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 17
A biologist keeps a specimen of his favorite beetle embedded in a cube of polystyrene plastic. The hapless bug appears to be 2.0 cm within the plastic. What is the beetle's actual distance beneath the surface?
Verified step by step guidance1
Step 1: Identify the concept involved in the problem. This problem deals with the refraction of light and the apparent depth versus actual depth phenomenon. The apparent depth is the depth perceived by an observer due to the bending of light as it passes through a medium with a different refractive index.
Step 2: Write down the formula that relates apparent depth and actual depth. The formula is: , where is the apparent depth, is the real (actual) depth, and is the refractive index of the medium.
Step 3: Rearrange the formula to solve for the actual depth. The equation becomes: . This allows us to calculate the real depth using the apparent depth and the refractive index.
Step 4: Determine the refractive index of polystyrene plastic. The refractive index of polystyrene is approximately . This value will be used in the calculation.
Step 5: Substitute the given values into the formula. The apparent depth is , and the refractive index is . Multiply these values to find the actual depth: . Perform the multiplication to find the result.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Refraction of Light
Refraction is the bending of light as it passes from one medium to another with a different density. In this scenario, light travels from the polystyrene plastic to the air, causing the apparent position of the beetle to differ from its actual position. The degree of bending depends on the refractive indices of the two materials involved.
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03:46
Index of Refraction
Refractive Index
The refractive index is a dimensionless number that describes how light propagates through a medium. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. For polystyrene, the refractive index is typically around 1.59, which affects how deep the beetle appears when viewed from outside the plastic.
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03:46Index of Refraction
Apparent Depth
Apparent depth refers to the perceived depth of an object submerged in a medium, which can differ from its actual depth due to refraction. The formula for calculating the apparent depth involves the actual depth and the refractive index of the medium. Understanding this concept is crucial for determining the true position of the beetle within the polystyrene.
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07:49Ray Diagrams for Convex Mirrors
Related Practice
Textbook Question
An underwater diver sees the sun 50° above horizontal. How high is the sun above the horizon to a fisherman in a boat above the diver?
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Textbook Question
A costume jewelry pendant made of cubic zirconia is submerged in oil. A light ray in the oil strikes one face of the zirconia crystal at an angle of incidence of 25°. Once inside, what is the ray's angle with respect to the face of the crystal?
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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
To a fish in an aquarium, the 4.00-mm-thick walls appear to be only 3.50 mm thick. What is the index of refraction of the walls?
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Textbook Question
The glass core of an optical fiber has an index of refraction 1.60. The index of refraction of the cladding is 1.48. What is the maximum angle a light ray can make with the wall of the core if it is to remain inside the fiber?
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