Ch 33: The Nature and Propagation of Light

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 33: The Nature and Propagation of Light

문제 3b

33장, 문제 3b

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

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.