Textbook Question
It is 165 cm from your eyes to your toes. You're standing 200 cm in front of a tall mirror. How far is it from your eyes to the image of your toes?
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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 12
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?
Verified step by step guidance1
Identify the relevant physics concept: This problem involves the refraction of light, which is governed by Snell's Law. Snell's Law is expressed as: , where and are the refractive indices of the two media, and and are the angles of incidence and refraction, respectively.
Determine the refractive indices: Look up the refractive index of oil () and cubic zirconia (). For example, the refractive index of oil is approximately 1.46, and the refractive index of cubic zirconia is approximately 2.15.
Apply Snell's Law: Substitute the known values into Snell's Law. For this problem, , , and . The equation becomes: .
Solve for the angle of refraction: Rearrange the equation to isolate : . Then, calculate by taking the inverse sine of the result: .
Interpret the result: The angle is the angle of refraction inside the cubic zirconia. To find the ray's angle with respect to the face of the crystal, subtract from 90°: . This gives the desired angle.
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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 how light rays change direction when they pass from one medium to another. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant and is equal to the ratio of the velocities of light in the two media. This principle is essential for determining the angle of the light ray as it enters the cubic zirconia from the oil.
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Snell's Law
Refractive Index
The refractive index is a dimensionless number that describes how fast light travels in a medium compared to its speed in a vacuum. Each material has a specific refractive index, which affects how much light bends when entering or exiting the material. For cubic zirconia and oil, knowing their refractive indices is crucial for applying Snell's Law to find the angle of refraction.
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Angle of Incidence and Angle of Refraction
The angle of incidence is the angle between the incoming light ray and the normal (perpendicular) line to the surface at the point of incidence. The angle of refraction is the angle between the refracted ray and the normal. Understanding these angles is vital for calculating how the light ray behaves as it transitions from oil into the cubic zirconia crystal.
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Related Practice
Textbook Question
A 1.0-cm-thick layer of water stands on a horizontal slab of glass. A light ray in the air is incident on the water 60° from the normal. What is the ray's direction of travel in the glass?
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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 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?
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Textbook Question
When you look into your car's 5.0-cm-tall rear-view mirror from 35 cm away, the front of a bus, from the ground to the roof, exactly fills the mirror. If the bus is 17 m from the mirror, how tall is the bus?
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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