Velocity of red light vs. blue light in water - qualitative reasoning?

In summary: I'll try to be more concise in future.In summary, sources say red light is faster in water than blue light, but nearly all descriptions/explanations depend on refractive indices and 'bending' to show that blue light is slowed to a greater extent. Instead, I'm wondering if a more precise explanation based on dispersion is possible b/c every time I attempt to reason out this fact based on group velocities, I get the opposite conclusion. My reasoning is that water is a dispersive material, so frequency w is non-linear wrt wave number k. Group velocity is dw/dk and always less than c, but the slope of the graph increases with k so group velocity is higher at lower wavelengths. This
  • #1
vvarma
4
0
Every source I have referred to says red light is faster in water than blue light. However, nearly all descriptions/explanations depend on refractive indices and 'bending' to show that blue light is slowed to a greater extent. Instead, I'm wondering if a more precise explanation based on dispersion is possible b/c every time I attempt to reason out this fact based on group velocities, I get the opposite conclusion.

My reasoning: Water is a dispersive material so frequency w is non-linear wrt wave number k. Group velocity is dw/dk and always less than c [sanity check] but the slope of the graph increases with k so group velocity is higher at lower wavelengths [k inversely proportional to lambda] which seems to imply that wave packets of lower wavelength should have a faster speed in water...

Am I using the dispersion relationship of w-k wrongly or is the group velocity not the same as the velocity of propagation [I'm fairly confident it is since number sources cite it as the speed that energy/information of the wave travel]?

Should I use phase velocity w/k instead? I have strong doubts given a) it always exceeds c and b) that dispersive wave means that w/k not equal to dw/dk = v. However, if I do use it, I get the correct connection of greater phase velocity for great wavelength.

I have a feeling that though I understand the terms and concepts to some degree, I can't draw the connection I want to b/c I'm lacking some other tool. Can you even draw the conclusion that vred > vblue in water knowing only w-k relationship?
 
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  • #2
The classical dispersion theory of em. waves in media is enough to understand the principle properties of light in media. A very good source about this is

A. Sommerfeld, Lectures on Theoretical Physics, Vol. IV (Optics)

There also wave propagation in the case of anomalous dispersion, where the phase velocity is greater than the in vacuo speed of light, is thoroughly discussed in a very elegant manner.
 
  • #3
The ratio of omega to k is the phase velocity.

Just remember that phase and group velocities have inverse relationship relative to c. Thus your reasoning when applied to phase velocity -- -red has lower phase velocity-- reverses to --red has higher group velocity--.
 
  • #4
@vanhees71 I'll definitely check out that source. Thank you.

@jambaugh Thanks for the reciprocal argument. It seems possible to me that I might be using the wrong w-k relationship to show this result due to a mislabeling on the part of my professor. Just to verify: is the graph of w(k) for water [and transparent materials in general] at all similar to w2=wp2+c2k2 because this is what my [incorrect] analysis is based on. If so, do you potentially have the correct w(k) from which to draw the wanted results?
 
  • #5
when monochromatic light as in red and blue light go through water their frequency remains constant so,the velocity depends on wavelength only .since blue light has smaller wavelength than red its velocity is also less than that of reds.
 
  • #6
tdev said:
when monochromatic light as in red and blue light go through water their frequency remains constant so,the velocity depends on wavelength only .since blue light has smaller wavelength than red its velocity is also less than that of reds.

Please try not to reply to 2 1/2 year old threads. :biggrin:
 
  • #7
Drakkith said:
Please try not to reply to 2 1/2 year old threads. :biggrin:
lol,i didnt see the date tanx for telling.
 
  • #8
From the mathpages reference on group.phase and signal velocity :
The refractive index is a function of frequency, like permittivity, resulting in the dispersion of colors seen in a prism
dω/dk = c/n - ck/n2 dn/dk
Hence any modulation of an electromagnetic wave in this medium will propagate at the group velocity: Vg = Vp [1 - k/n dn/dk] Since n increases with the wave number k and therefore frequency - this is why the blue component of white light is refracted more than red.
From Huygens' Construction for the refractive index : sin∅1/sin∅212 = v1/v2 . In the geometric optics diagram
Huygen shows the the wavelength and velocity from air to a material medium decreases : λ21v2/v1
Can these two explanations for the refractive index , (dispersion + group velocity ) and Huygens
geometric optics that show the wavelength and therefore velocity in the medium decreased, be unified with a common mechanism ?

Oh sorrey just noticed date !
 
Last edited:

1. What is the difference between the velocity of red light and blue light in water?

The velocity of red light and blue light in water differs due to their different wavelengths. Red light has a longer wavelength and therefore travels slower in water compared to blue light which has a shorter wavelength and travels faster.

2. Why does red light travel slower in water compared to blue light?

This is due to the phenomenon of refraction, where the speed of light changes as it passes through different mediums. The refractive index of water is higher for red light compared to blue light, causing red light to slow down more in water than blue light.

3. How does the velocity of light in water affect color perception?

The difference in velocity of red light and blue light in water can cause a shift in the perceived color of objects underwater. This is because the color we see is determined by the wavelengths of light that are reflected off the object. As red light travels slower in water, it is more likely to be absorbed by the water, resulting in a shift towards blue-green hues.

4. Can the velocity of light in water be affected by other factors?

Yes, the velocity of light in water can be affected by factors such as temperature, pressure, and salinity. Changes in these factors can alter the refractive index of water and therefore affect the speed of light.

5. Is the velocity of light in water the same for all wavelengths?

No, the velocity of light in water varies for different wavelengths. This is known as dispersion, where different wavelengths are refracted at different angles, causing them to travel at different speeds. This is also the reason why we see a rainbow when white light is dispersed by water droplets in the atmosphere.

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