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

Click For Summary
The discussion focuses on the dependence of phase velocity (vp) on wavelength (λ) in glass, highlighting that glass is a dispersive medium. The phase velocity is expressed as vp = c/n, where n is the refractive index, which varies with wavelength. The participant is uncertain about how to derive vp(λ) and whether the velocity in the equation n = c/v refers to vp or another velocity. They propose that the derivative dvp/dλ is positive, indicating that phase velocity increases with wavelength. The conversation emphasizes the need for clarity in differentiating the various velocities involved in the equations.
Kavorka
Messages
95
Reaction score
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
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:
it seems right. Have you got your answer yet?
 

Thread 'Coulomb's force vs the Lorentz force'

Beams of electrons and protons move parallel to each other in the same direction. They ______. a. attract each other. b. repel each other. c. neither attract nor repel. d. the force of attraction or repulsion depends upon the speed of the beams. This is a previous-year-question of CBSE Board 2023. The answer key marks (b) as the right option. I want to know why we are ignoring Coulomb's force?
View full post »
Thread 'Struggling to make relation between elastic force and height'

Thread 'Struggling to make relation between elastic force and height'

Hello guys this is what I tried so far. I used the UTS to calculate the force it needs when the rope tears. My idea was to make a relationship/ function that would give me the force depending on height. Yeah i couldnt find a way to solve it. I also thought about how I could use hooks law (how it was given to me in my script) with the thought of instead of having two part of a rope id have one singular rope from the middle to the top where I could find the difference in height. But the...
View full post »

Thread 'Speed of moth related to Doppler Effect'

I treat this question as two cases of Doppler effect. (1) When the sound wave travels from bat to moth Speed of sound = 222 x 1.5 = 333 m/s Frequency received by moth: $$f_1=\frac{333+v}{333}\times 222$$ (2) When the sound wave is reflected from moth back to bat Frequency received by bat (moth as source and bat as observer): $$f_2=\frac{333}{333-v}\times f_1$$ $$230.3=\frac{333}{333-v}\times \frac{333+v}{333}\times 222$$ Solving this equation, I get ##v=6.1## m/s but the answer key is...
View full post »

Similar threads

What is the phase velocity of light in glass?
Replies
2
Views
2K
Why Does Light Diminish with a Phase Difference of 5λ?
Replies
6
Views
907
What are the speeds of P and M while riding Ents and playing catch with rings?
Replies
18
Views
2K
Phase velocity of EM radiation in free space
Replies
7
Views
4K
Group and phase velocity of a wave
Replies
2
Views
1K
Total Internal Reflection and Transmitted Wavelength
Replies
1
Views
866
Phase difference after passing through liquid and glass
Replies
2
Views
2K
Doppler effect and acceleration of source
Replies
5
Views
2K
Phase difference between points on wall
Replies
4
Views
3K
What Visible Wavelengths Cause Maximum Constructive Interference in a Thin Film?
Replies
1
Views
3K