Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Problem 2136

What is the ratio of velocities of light rays of wavelengths $4000^{\circ} \mathrm{A}\( and \)8000^{\circ} \mathrm{A}$ in vacuum? (A) \(1: 2\) (B) \(1: 1\) (C) \(2: 1\) (D) cannot be determined

Short Answer

Expert verified
The ratio between the velocities of light rays with given wavelengths is equal to the ratio of their frequencies. We find that the ratio of frequencies for the wavelengths \(4000^{\circ} \mathrm{A}\) and \(8000^{\circ} \mathrm{A}\) is \(2:1\). Therefore, the correct answer is (C) \(2:1\).

Step by step solution

01

Determine the relationship between speed, frequency, and wavelength of light in vacuum.

The relationship between the speed of light (\(v\)), its frequency (\(f\)), and its wavelength (\(\lambda\)) in vacuum is given by the formula: \(v = f\lambda\)
02

Identify the constant speed of light in vacuum.

Regardless of the wavelength of light - the speed of light (\(c\)) in vacuum is always constant, with the value of: \(c = 3 \times 10^8 \ m/s\)
03

Calculate the frequency for the given wavelengths.

We want to find the ratio of velocities of light rays with wavelengths \(\lambda_1 = 4000^{\circ} \mathrm{A}\) and \(\lambda_2 = 8000^{\circ} \mathrm{A}\). Using the relationship \(v = f\lambda\), we have: \(f_1 = \frac{c}{\lambda_1}\) and \(f_2 = \frac{c}{\lambda_2}\)
04

Find the ratio of frequencies.

Now, let's find the ratio of frequencies \(f_1\) and \(f_2\). Here, we have: \(\frac{f_1}{f_2} = \frac{\frac{c}{\lambda_1}}{\frac{c}{\lambda_2}} = \frac{\lambda_2}{\lambda_1} = \frac{8000^{\circ} \mathrm{A}}{4000^{\circ} \mathrm{A}} = \frac{8000}{4000} = 2\)
05

Confirm the answer using the given options.

The ratio between the velocities of light rays with given wavelengths is equal to the ratio of their frequencies, which we found as \(2:1\). Therefore, the correct answer is (C) \(2:1\).

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

In an electromagnetic wave in free space, the direction of electric field vector \(E^{-}\) is along \(y\) axis and magnetic field vector \(\mathrm{B}^{-}\) is along \(\mathrm{z}\) axis then which of the following is true (A) $\left(\mathrm{E}^{-} \times \mathrm{B}^{-}\right) \times \mathrm{E}^{-}=1$ (B) $\left(\mathrm{E}^{-} \times \mathrm{B}^{-}\right) \times \mathrm{B}^{-}=1$ (C) $\left(\mathrm{E}^{-} \times \mathrm{B}^{-}\right) \times \mathrm{B}^{-}=0$ (D) none of these

What is the name associated with the equation \(E^{\longrightarrow} \cdot d t^{-}=-(d \Phi \beta / d t)\) (A) Gauss law for electricity (B) Gauss law for magnetism (C) ampere's law (D) faraday's law

The sun delivers \(10^{3} \mathrm{Wm}^{-2}\) of electromagnetic flux to earth's surface. The total power that is incident on a roof of dimension $8 \mathrm{~m} \times 20 \mathrm{~m}$ will be (A) \(4 \times 10^{5} \mathrm{w}\) (B) \(2.56 \times 10^{4} \mathrm{w}\) (C) \(6.4 \times 10^{5} \mathrm{w}\) (D) \(1.6 \times 10^{5} \mathrm{w}\)

If the direction of magnetic field \(\mathrm{B}^{\rightarrow}\) at some instant is along + ve \(Z\) direction and the electromagnetic wave is propagating along + ve \(\mathrm{X}\) direction, then the direction of electric field \(\mathrm{E}^{\rightarrow}\) at that instant is (A) along - ve Y direction (B) along + ve Y direction (C) along + ve \(\mathrm{X}\) direction (B) along - ve \(\mathrm{X}\) direction

A new system of unit is evolved in which the values of \(\mu_{0}\) and \(\varepsilon_{0}\) are 2 and 8 respectively. Then the speed of light in this system will be (A) \(0.25\) (B) \(0.5\) (C) \(0.75\) (D) 1
See all solutions

Recommended explanations on English Textbooks

Text Comparison

Read Explanation

Blog

Read Explanation

Multiple Choice Questions

Read Explanation

Discourse

Read Explanation

English Grammar

Read Explanation

Essay Prompts

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