Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 22: Problem 57

A star is moving away from Earth at a speed of $2.4 \times 10^{8} \mathrm{m} / \mathrm{s} .\( Light of wavelength \)480 \mathrm{nm}$ is emitted by the star. What is the wavelength as measured by an Earth observer?

Short Answer

Expert verified
Answer: The redshifted wavelength of the light as observed from Earth is approximately 864 nm.

Step by step solution

01

Understand the redshift formula

The redshift formula relates the initial wavelength (λ₀) of light emitted by a moving object and the observed wavelength (λ), taking into account the relative speed (v) of the observer and the object. The redshift formula is given by: \(λ = λ₀\left(1+\frac{v}{c}\right)\) where c is the speed of light in vacuum \(c = 3 × 10^8 m/s \). In this exercise, we are given the initial wavelength of light (λ₀) and the speed of the star (v) moving away from Earth. We need to find the redshifted wavelength (λ) as seen by an observer on Earth.
02

List the given values

We are given the following values: Initial Wavelength (λ₀): \(480 nm = 480 × 10^{-9} m\) Speed of the Star (v): \(2.4 × 10^8 m/s\) Speed of Light (c): \(3 × 10^8 m/s\) We need to find the observed wavelength (λ).
03

Calculate the redshifted wavelength

Plug in the given values into the redshift formula: \(λ = λ₀\left(1+\frac{v}{c}\right) = (480 × 10^{-9})\left(1+\frac{2.4 × 10^8}{3 × 10^8}\right)\)
04

Solve for the observed wavelength

Calculate the observed wavelength by solving the equation: \(λ = (480 × 10^{-9})\left(1+\frac{2.4 × 10^8}{3 × 10^8}\right) = (480 × 10^{-9})(1 + 0.8) ≈ (480 × 10^{-9})(1.8) = 864 × 10^{-9} m\)
05

Convert the result to nanometers

Convert the wavelength from meters back to nanometers: \(λ = 864 × 10^{-9} m = 864 nm\) The wavelength of the light as measured by an Earth observer is approximately 864 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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

What is the frequency of the microwaves in a microwave oven? The wavelength is \(12 \mathrm{cm}\)
A police car's radar gun emits microwaves with a frequency of $f_{1}=36.0 \mathrm{GHz}$. The beam reflects from a speeding car, which is moving away at \(43.0 \mathrm{m} / \mathrm{s}\) with respect to the police car. The frequency of the reflected microwave as observed by the police is \(f_{2} .\) (a) Which is larger, \(f_{1}\) or \(f_{2} ?\) (b) Find the frequency difference \(f_{2}-f_{1}\) [Hint: There are two Doppler shifts. First think of the police as source and the speeder as observer. The speeding car "retransmits" a reflected wave at the same frequency at which it observes the incident wave. \(]\)
A 60.0 -m \(\mathrm{W}\) pulsed laser produces a pulse of EM radia tion with wavelength \(1060 \mathrm{nm}\) (in air) that lasts for 20.0 ps (picoseconds). (a) In what part of the EM spectrum is this pulse? (b) How long (in centimeters) is : single pulse in air? (c) How long is it in water \((n=1.33) \equiv\) (d) How many wavelengths fit in one pulse? (e) What is the total electromagnetic energy in one pulse?
A polarized beam of light has intensity \(I_{0} .\) We want to rotate the direction of polarization by \(90.0^{\circ}\) using polarizing sheets. (a) Explain why we must use at least two sheets. (b) What is the transmitted intensity if we use two sheets, each of which rotates the direction of polarization by \(45.0^{\circ} ?\) (c) What is the transmitted intensity if we use four sheets, each of which rotates the direction of polarization by \(22.5^{\circ} ?\)
The electric field of an EM wave is given by \(E_{z}=\) $E_{\mathrm{m}} \sin (k y-\omega t+\pi / 6), E_{x}=0,\( and \)E_{z}=0 .$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the magnetic field of this wave.
See all solutions

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Read Explanation

Wave Optics

Read Explanation

Nuclear Physics

Read Explanation

Waves Physics

Read Explanation

Magnetism

Read Explanation

Modern Physics

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.

Sign-up for free