/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 Light with a frequency of \(5.80... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 33: Problem 4

Light with a frequency of \(5.80 \times 10^{14} \mathrm{Hz}\) travels in a block of glass that has an index of refraction of \(1.52 .\) What is the wavelength of the light (a) in vacuum and (b) in the glass?

Short Answer

Expert verified
(a) 517 nm in vacuum; (b) 340 nm in glass.

Step by step solution

01

Wavelength in Vacuum

To find the wavelength of light in a vacuum, we use the formula for the speed of light:\[\lambda_0 = \frac{c}{f}\]where \(\lambda_0\) is the wavelength in a vacuum, \(c\) is the speed of light in a vacuum \((3.00 \times 10^8 \text{ m/s})\), and \(f\) is the frequency of the light. Substituting the known values:\[\lambda_0 = \frac{3.00 \times 10^8 \text{ m/s}}{5.80 \times 10^{14} \text{ Hz}} = 5.17 \times 10^{-7} \text{ m} = 517 \text{ nm}\]So, the wavelength in a vacuum is 517 nm.
02

Calculate Wavelength in Glass

To find the wavelength of the light in the glass, we use the formula:\[\lambda_{n} = \frac{\lambda_0}{n}\]where \(\lambda_n\) is the wavelength in the medium, \(\lambda_0\) is the wavelength in a vacuum, and \(n\) is the index of refraction of the medium. Substituting the known values:\[\lambda_{n} = \frac{517 \text{ nm}}{1.52} = 340 \text{ nm}\]Thus, the wavelength of the light in the glass is 340 nm.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Wavelength
Wavelength is a fundamental concept in wave optics. It represents the distance between two consecutive peaks (or troughs) of a wave. This distance helps determine the wave's properties, such as its color in the case of light. For light traveling in a vacuum, the wavelength can be determined using the formula:\[\lambda_0 = \frac{c}{f}\] where \(\lambda_0\) is the wavelength in a vacuum, \(c\) is the speed of light \((3.00 \times 10^8 \text{ m/s})\), and \(f\) is the frequency. When light speeds through different mediums, its wavelength changes, but the frequency remains constant. This change is due to the wave's new speed in the given medium.
Frequency
Frequency refers to the number of wave cycles that pass a particular point in one second. It is measured in hertz (Hz). In the context of light waves, frequency determines the color of the light. The equation linking frequency and wavelength in a vacuum is:\[f = \frac{c}{\lambda_0}\]where \(\lambda_0\) is the wavelength and \(c\) is the speed of light.
  • High frequency means a shorter wavelength and more cycles per second.
  • Low frequency results in a longer wavelength and fewer cycles per second.
Understanding frequency is key to comprehending how light behaves and interacts with different media.
Index of Refraction
The index of refraction, often represented by \(n\), describes how much light bends as it enters a new medium. This value is a ratio comparing the speed of light in a vacuum to its speed in the substance. It is calculated using the formula:\[n = \frac{c}{v}\]where \(v\) is the speed of light in the medium.For instance, in glass where the index is 1.52, light travels more slowly than in a vacuum. This slowdown results in a shorter wavelength but the same frequency. This principle is crucial in designing lenses and other optical devices.
Medium
A medium is any substance through which light can travel. Different media affect the way light propagates. In wave optics, the medium's properties (like its index of refraction) significantly affect the wavelength and speed of light.
  • When moving from a vacuum to glass, the speed of light decreases.
  • This change alters the wavelength while keeping the frequency constant.
Understanding different media allows us to appreciate phenomena like refraction and allows for practical applications in technology like fiber optics and cameras. Different media transform how we see and understand waves.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Light is incident normally on the short face of a \(30^{\circ}-\) \(60^{\circ}-90^{\circ}\) prism (Fig. \(\mathrm{P} 33.52 ) . \mathrm{A}\) drop of liquid is placed on the hypotenuse of the prism. If the index of refraction of the prism is \(1.62,\) find the maximum index that the liquid may have if the light is to be totally reflected.

In a material having an index of refraction \(n,\) a light ray has frequency \(f,\) wavelength \(\lambda,\) and speed \(v .\) What are the frequency, wavelength, and speed of this light (a) in vacuum and (b) in a material having refractive index \(n^{\prime} ?\) In each case, express your answers in terms of only \(f, \lambda, v, n,\) and \(n^{\prime} .\)

A glass plate 2.50 \(\mathrm{mm}\) thick, with an index of refraction of 1.40 , is placed between a point source of light with wavelength 540 \(\mathrm{nm}\) (in vacuum) and a screen. The distance from source to screen is 1.80 \(\mathrm{cm} .\) How many wavelengths are there between the source and the screen?

The refractive index of a certain glass is \(1.66 .\) For what incident angle is light reflected from the surface of this glass completely polarized if the glass is immersed in (a) air and (b) water?

A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of \(\theta_{a}=36.2^{\circ},\) the ray refracted into the water makes an angle of \(49.8^{\circ}\) with the normal to the interface. What is the smallest value of the incident angle \(\theta_{a}\) for which none of the ray refracts into the water?
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Fields in Physics

Read Explanation

Magnetism

Read Explanation

Measurements

Read Explanation

Radiation

Read Explanation

Astrophysics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.