What is the general dependence of the phase velocity on wavelength in glass?

In summary, the conversation discusses the group and phase velocities of light in a dispersive medium, specifically in ordinary glass. The group velocity can be expressed as vg = vp - λ(dvp/dλ) starting from Equation 5-1, which relates frequency, energy, and Planck's constant. In part b, the general dependence of vp on λ in glass is discussed and it is determined that dvp/dλ is positive. The conversation also touches on the confusion between different velocities and terms and how to find vp(λ). Finally, the summary presents a possible solution for part b, where vp is calculated using the velocity of light and the refractive index, and it is concluded that dvp/dλ is positive.
  • #1
Kavorka
95
0

Homework Statement


a) Starting from Equation 5-1, show that the group velocity can also be expressed as: vg = vp - λ(dvp/dλ)

b) The phase velocity of each wavelength of white light moving through ordinary glass is a function of the wavelength; that is, glass is a dispersive medium. What is the general dependence of vp on λ in glass? Is dvp/dλ positive or negative?

I'm mostly concerned about part b, but I have a question about part a as well.

Homework Equations


Equation 5-1: f = E/h
vp = ω/k = fλ
vg = vp + k(dvp/dk)
n = c/v

3. The Attempt at a Solution

a) Using the last two equations I listed and just plugging in what k equals as well as what dk equals after differentiating the second equation in terms of wavelength, it is very easy to see how to get the the equation they want from the equation we were given in class. What I don't understand is how Eq. 5-1 comes into it, and what they want you to show "starting from" that equation. Any ideas?

b) I feel like this is simple but I'm not sure how to start because I am confusing all the different velocities and terms. Once I have vp(λ) I'll differentiate it to easily answer the second part. Any hints on how to begin to find vp(λ)? Is the v in n = c/v equal to vp, or is it equal to the actual velocity of the particle which is 2vp?
 
Physics news on Phys.org
  • #2
anyone?

This is what I came up with for b:

vp = c/n
c = fλ

vp = fλ/n

dvp/dλ = f/n = positive

I have no idea if this is right. Seems too simple.
 
Last edited:
  • #3
it seems right. Have you got your answer yet?
 

1. What is phase velocity in glass?

Phase velocity in glass is the speed at which an electromagnetic wave travels through a glass material. It is determined by the properties of the glass, such as its refractive index and density.

2. How does phase velocity differ from group velocity in glass?

Phase velocity and group velocity are two different ways to measure the speed of an electromagnetic wave. Phase velocity refers to the speed at which the wave's phase (or cycle) travels, while group velocity refers to the speed at which the wave's energy travels. In glass, the two velocities can differ due to the material's dispersive properties.

3. How is phase velocity affected by the composition of glass?

The composition of glass, specifically its refractive index, can greatly affect the phase velocity of an electromagnetic wave passing through it. Different types of glass, such as leaded glass or borosilicate glass, have different refractive indices which can impact the phase velocity of light passing through them.

4. Can phase velocity in glass be controlled or manipulated?

Yes, the phase velocity in glass can be controlled and manipulated through various methods. One way is by changing the composition of the glass, such as by adding dopants to alter its refractive index. Another method is by implementing special coatings or layers on the surface of the glass to alter its properties.

5. What are the practical applications of understanding phase velocity in glass?

Understanding phase velocity in glass is important in various fields, such as optics, telecommunications, and material science. It allows scientists and engineers to design and optimize devices and systems that use glass, such as lenses, optical fibers, and photonic devices. It also helps in understanding the behavior of light in different mediums, which can lead to advancements in technology and research.

Similar threads

Why Does Light Diminish with a Phase Difference of 5λ?
    • Introductory Physics Homework Help
Replies
6
Views
204
What is the phase velocity of light in glass?
    • Introductory Physics Homework Help
Replies
2
Views
2K
What are the speeds of P and M while riding Ents and playing catch with rings?
    • Introductory Physics Homework Help
Replies
18
Views
2K
Total Internal Reflection and Transmitted Wavelength
    • Introductory Physics Homework Help
Replies
1
Views
132
Doppler effect and acceleration of source
    • Introductory Physics Homework Help
Replies
5
Views
1K
Inside glass, can I apply relativity of speed for light?
    • Introductory Physics Homework Help
Replies
4
Views
643
Phase velocity of EM radiation in free space
    • Introductory Physics Homework Help
Replies
7
Views
4K
Phase difference between points on wall
    • Introductory Physics Homework Help
Replies
4
Views
3K
Group and phase velocity of a wave
    • Introductory Physics Homework Help
Replies
2
Views
1K
Phase difference after passing through liquid and glass
    • Introductory Physics Homework Help
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top