Domanda del libro di testo
A point source of light illuminates an aperture 2.0 m away. A 12.0-cm-wide bright patch of light appears on a screen 1.0 m behind the aperture. How wide is the aperture?
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Ch 34: Ray Optics
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 34, Problema 1b
What distance does light travel in water, glass, and cubic zirconia during the time that it travels 1.0 m in vacuum?
Guida verificata passo dopo passo1
Determine the speed of light in a vacuum, which is approximately \( c = 3.0 \times 10^8 \, \text{m/s} \). This is the reference speed for light in a vacuum.
Identify the refractive indices of water, glass, and cubic zirconia. These values are typically \( n_{\text{water}} \approx 1.33 \), \( n_{\text{glass}} \approx 1.5 \), and \( n_{\text{cubic zirconia}} \approx 2.2 \). The refractive index \( n \) relates the speed of light in a medium to the speed of light in a vacuum.
Use the relationship \( v = \frac{c}{n} \) to calculate the speed of light in each medium. Here, \( v \) is the speed of light in the medium, \( c \) is the speed of light in a vacuum, and \( n \) is the refractive index of the medium.
Calculate the time it takes for light to travel 1.0 m in a vacuum using \( t = \frac{d}{c} \), where \( d = 1.0 \, \text{m} \) and \( c = 3.0 \times 10^8 \, \text{m/s} \). This time will be the same for light traveling in the other media.
Determine the distance light travels in each medium using \( d = v \cdot t \), where \( v \) is the speed of light in the medium (calculated in step 3) and \( t \) is the time calculated in step 4. Perform this calculation for water, glass, and cubic zirconia to find the respective distances.
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Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Speed of Light
The speed of light in a vacuum is approximately 299,792 kilometers per second (or about 3.00 x 10^8 m/s). This constant is fundamental in physics and serves as a benchmark for understanding how light behaves in different media. When light travels through materials like water, glass, or cubic zirconia, its speed decreases due to interactions with the atoms in those materials.
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Percorso guidato
06:03
The Doppler Effect (Light)
Refractive Index
The refractive index is a dimensionless number that describes how light propagates through a medium compared to its speed in a vacuum. It is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. For example, water has a refractive index of about 1.33, meaning light travels slower in water than in vacuum, which affects the distance light travels in that medium over a given time.
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03:46Index of Refraction
Distance Calculation in Different Media
To determine the distance light travels in various media during the time it takes to travel 1.0 m in vacuum, one must use the formula: distance = speed × time. The time taken for light to travel 1.0 m in vacuum can be calculated, and then this time can be used with the speed of light in each medium (derived from the refractive index) to find the corresponding distances in water, glass, and cubic zirconia.
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04:15Calculating Dot Product Using Vector Components
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