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 34
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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Identify the relevant physics principle: This problem involves Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of two media. The formula is: , where and are the indices of refraction of the first and second medium, and and are the angles of incidence and refraction, respectively.
Assign known values: The index of refraction of air is approximately . The angle of incidence is , and the angle of refraction in the liquid is . The goal is to find the liquid's index of refraction, .
Rearrange Snell's Law to solve for the unknown index of refraction: .
Substitute the known values into the equation: .
Use a scientific calculator to compute the sine values for the angles and divide them to find . Ensure your calculator is in degree mode when calculating the sine of the angles.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Snell's Law
Snell's Law describes the relationship between the angles of incidence and refraction when a wave passes between two different media. It is mathematically expressed as n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the indices of refraction of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively. This law is fundamental in understanding how light behaves at the interface of different materials.
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Snell's Law
Index of Refraction
The index of refraction (n) is a dimensionless number that describes how fast light travels in a medium compared to its speed in a vacuum. It is defined as n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium. A higher index indicates that light travels slower in that medium, which affects how light bends when entering or exiting the material.
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Angle of Incidence and Refraction
The angle of incidence is the angle between the incident ray and the normal line at the point of contact on the surface, while the angle of refraction is the angle between the refracted ray and the normal. These angles are crucial for applying Snell's Law to determine how light changes direction when transitioning between different media, such as air and liquid in this scenario.
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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 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.
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
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 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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