Textbook Question
A beam of light has a wavelength of 650 nm in vacuum. What is the wavelength of these waves in the liquid?
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Ch 33: The Nature and Propagation of Light
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 33, Problem 5b
A light beam travels at 1.94 × 108 m/s in quartz. The wavelength of the light in quartz is 355 nm. If this same light travels through air, what is its wavelength there?
Verified step by step guidance1
First, understand that the speed of light in a medium is given by the equation: , where is the speed of light in vacuum (approximately ) and is the refractive index of the medium.
Calculate the refractive index of quartz using the given speed of light in quartz: . Substitute and .
Once you have the refractive index of quartz, use the relationship between wavelength and refractive index: . Here, is the wavelength in quartz, which is given as 355 nm.
To find the wavelength of light in air, note that the refractive index of air is approximately 1. Therefore, the wavelength in air is approximately equal to the wavelength in vacuum.
Use the relationship to calculate the wavelength in air, substituting and .
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Speed of Light in Different Mediums
The speed of light varies depending on the medium it travels through due to the medium's refractive index. In a vacuum, light travels at approximately 3.00 x 10^8 m/s, but in materials like quartz, it slows down. Understanding how the refractive index affects light speed is crucial for calculating changes in wavelength when light transitions between mediums.
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Wavelength and Frequency Relationship
The wavelength of light is inversely proportional to its frequency, given by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. When light moves from one medium to another, its speed and wavelength change, but its frequency remains constant. This relationship helps determine the new wavelength when light enters a different medium.
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Refractive Index
The refractive index of a medium quantifies how much light slows down 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. Knowing the refractive index allows us to calculate the speed and wavelength of light in different materials, essential for solving problems involving light transition between mediums.
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Related Practice
Textbook Question
Two plane mirrors intersect at right angles. A laser beam strikes the first of them at a point 11.5 cm from their point of intersection, as shown in Fig. E33.1. For what angle of incidence at the first mirror will this ray strike the midpoint of the second mirror (which is 28.0 cm long) after reflecting from the first mirror?
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Textbook Question
Light of a certain frequency has a wavelength of 526 nm in water. What is the wavelength of this light in benzene?
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Textbook Question
Light traveling in air is incident on the surface of a block of plastic at an angle of 62.7° to the normal and is bent so that it makes a 48.1° angle with the normal in the plastic. Find the speed of light in the plastic.
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Textbook Question
(a) A tank containing methanol has walls 2.50 cm thick made of glass of refractive index 1.550. Light from the outside air strikes the glass at a 41.3° angle with the normal to the glass. Find the angle the light makes with the normal in the methanol. (b) The tank is emptied and refilled with an unknown liquid. If light incident at the same angle as in part (a) enters the liquid in the tank at an angle of 20.2° from the normal, what is the refractive index of the unknown liquid?
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