Ch 33: The Nature and Propagation of Light

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 33: The Nature and Propagation of Light

Problem 3b

Chapter 33, Problem 3b

A beam of light has a wavelength of 650 nm in vacuum. What is the wavelength of these waves in the liquid?

Verified step by step guidance

First, understand that the wavelength of light changes when it moves from one medium to another due to the change in speed. The speed of light in a medium is given by the equation:

v = \frac{c}{n}

, where

c

is the speed of light in vacuum and

n

is the refractive index of the medium.

Next, recall the relationship between the speed of light, frequency, and wavelength:

v = f λ

, where

v

is the speed of light in the medium,

f

is the frequency, and

λ

is the wavelength.

Since the frequency of light remains constant when transitioning between media, use the equation:

f = \frac{c}{λ}

in vacuum and

f = \frac{v}{λ'}

in the liquid, where

λ'

is the wavelength in the liquid.

Equate the two expressions for frequency:

\frac{c}{λ} = \frac{v}{λ'}

. Substitute

v

with

\frac{c}{n}

to get:

\frac{c}{λ} = \frac{\frac{c}{n}}{λ'}

Solve for

λ'

by rearranging the equation:

λ' = \frac{λ}{n}

. This gives the wavelength of the light in the liquid.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Wavelength

Wavelength is the distance between consecutive peaks of a wave, typically measured in nanometers for light. It determines the color of visible light and is affected by the medium through which the light travels. In a vacuum, light travels at its maximum speed, and its wavelength is unchanged.

Refractive Index

The refractive index of a medium is a measure of how much the speed of light is reduced inside the medium compared to its speed in a vacuum. It is a dimensionless number that indicates how much light bends when entering the medium. A higher refractive index means light travels slower, affecting its wavelength.

Speed of Light in Different Media

The speed of light varies depending on the medium it travels through. In a vacuum, light travels at approximately 299,792 km/s, but this speed decreases in denser media like liquids or solids. The change in speed results in a change in wavelength, while the frequency remains constant.

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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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