Domanda del libro di testo
A diffraction grating produces a first-order maximum at an angle of 20.0°. What is the angle of the second-order maximum?
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Ch 33: Wave 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 33, Problema 7
In a double-slit experiment, the slit separation is 200 times the wavelength of the light. What is the angular separation (in degrees) between two adjacent bright fringes?
Guida verificata passo dopo passo1
Identify the formula for angular separation between adjacent bright fringes in a double-slit experiment: \( \Delta \theta = \arcsin\left( \frac{m \lambda}{d} \right) - \arcsin\left( \frac{(m-1) \lambda}{d} \right) \), where \( \lambda \) is the wavelength of light, \( d \) is the slit separation, and \( m \) is the fringe order.
Since the problem asks for the angular separation between two adjacent bright fringes, we can simplify the calculation by using the small-angle approximation: \( \Delta \theta \approx \frac{\lambda}{d} \). This is valid because \( \lambda \ll d \).
Substitute the given relationship between the slit separation and the wavelength: \( d = 200 \lambda \).
Replace \( d \) in the formula with \( 200 \lambda \): \( \Delta \theta \approx \frac{\lambda}{200 \lambda} \).
Simplify the expression to find \( \Delta \theta \) in radians, and then convert it to degrees using the conversion factor \( 1 \text{ radian} = \frac{180}{\pi} \text{ degrees} \).
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Double-Slit Experiment
The double-slit experiment demonstrates the wave nature of light through interference patterns. When coherent light passes through two closely spaced slits, it creates a series of bright and dark fringes on a screen due to constructive and destructive interference. The pattern's characteristics depend on the wavelength of the light and the distance between the slits.
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Percorso guidato
12:00
Young's Double Slit Experiment
Wavelength and Slit Separation
In the context of the double-slit experiment, the slit separation relative to the wavelength of light is crucial for determining the interference pattern. When the slit separation is significantly larger than the wavelength, the angular separation between bright fringes can be calculated using the formula for angular position, which is influenced by the ratio of slit separation to wavelength.
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Percorso guidato
05:42Unknown Wavelength of Laser through Double Slit
Angular Separation of Fringes
The angular separation between adjacent bright fringes in a double-slit experiment can be calculated using the formula θ = λ/d, where θ is the angular separation, λ is the wavelength, and d is the slit separation. This relationship shows how the spacing of the fringes is directly proportional to the wavelength and inversely proportional to the slit separation, allowing for precise predictions of fringe locations.
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Percorso guidato
09:05Number of Dark Fringes on a Screen
Pratica correlata
Domanda del libro di testo
Light of wavelength 550 nm illuminates a double slit, and the interference pattern is observed on a screen behind the slit. The third maximum is measured to be 3.0 cm from the central maximum. The slits are then illuminated with light of wavelength 440 nm. How far is the fourth maximum from the central maximum?
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Domanda del libro di testo
The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656 nm (red) and 486 nm (blue). Light from a hydrogen lamp illuminates a diffraction grating with 500 lines/mm, and the light is observed on a screen 1.50 m behind the grating. What is the distance between the first-order red and blue fringes?
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Domanda del libro di testo
A double-slit interference pattern is created by two narrow slits spaced 0.25 mm apart. The distance between the first and the fifth minimum on a screen 60 cm behind the slits is 5.5 mm. What is the wavelength (in nm) of the light used in this experiment?
1817
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