# Speed of light versus wavelength

We know the speed of light is a constant but speed is just the measure of distance over time. If blue light has a shorter wavelength than red but covers the same distance / time does this mean that blue light has actually made a longer journey than red light in order to arrive simultaneously?

I Imagine two roads that start and finish at the same point. A 5 mile straight road and a 10 mile bending road . A car will have to travel twice as fast on the winding road in order to finish at the same time

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PeroK
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We know the speed of light is a constant but speed is just the measure of distance over time. If blue light has a shorter wavelength than red but covers the same distance / time does this mean that blue light has actually made a longer journey than red light in order to arrive simultaneously?
No.

Imagine two roads that start and finish at the same point. A 5 mile straight road and a 10 mile bending road . A car will have to travel twice as fast on the winding road in order to finish at the same time
That's true, but a car on a winding country road is a poor analogy for an electromagnetic wave.

DaveC426913
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The fact that blue light is a shorter wavelength doesn't mean it travelled a longer journey, any more than a compact car has to travel further than a limousine on a straight road.

Your winding road analogy is poor, the distance travelled by light is independent of the transverse motion. Light doesn't move like a slithering snake.

Compare it more to a car on a straight road with two kids in the back seat - on of them high on sugar.
Sugar kid bops around twice as fast, but that doesn't mean he literally travels a path twice as long and twice as fast.

rsk, nasu, hutchphd and 1 other person
The fact that blue light is a shorter wavelength doesn't mean it travelled a longer journey, any more than a compact car has to travel further than a limousine on a straight road.

Your winding road analogy is poor, the distance travelled by light is independent of the transverse motion. Light doesn't move like a slithering snake.

Compare it more to a car on a straight road with two kids in the back seat - on of them high on sugar.
Sugar kid bops around twice as fast, but that doesn't mean he literally travels a path twice as long and twice as fast.
In your analogy is each child in the backseat a different frequency / colour of light? Also what would the car be analogous with?

jbriggs444
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Imagine two roads that start and finish at the same point. A 5 mile straight road and a 10 mile bending road . A car will have to travel twice as fast on the winding road in order to finish at the same time
I am just guessing here at the reason for your expectation.

We often see light depicted in science videos or in textbooks as a sort of sine wave. For instance (picking a Google hit at random). https://physicsopenlab.org/2019/08/20/polarization-of-light/

It is easy to imagine that this means that the light is actually following the wavy path instead of propagating along a straight line. That imagination is dead wrong.

Depictions of light as a sine wave along the x axis are using the x to measure distance. But they are using the y and z axes to depict transverse electric field strength, not transverse displacement. The light wave propagates in a straight line regardless of frequency.

russ_watters, davenn, PeroK and 1 other person
Halc
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Compare it more to a car on a straight road with two kids in the back seat - on of them high on sugar.
Sugar kid bops around twice as fast, but that doesn't mean he literally travels a path twice as long and twice as fast.
If enough sugar and a slow enough car, it very much does mean that in the frame of the road, he literally travels a path twice as long and twice as fast as the sleeping kid, which is why the kids in the car analogy is terrible.

jbriggs444 expressed it better.

DaveC426913
davenn
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We know the speed of light is a constant

that needs to be qualified
The speed of light varies depending on the medium that the EM wave is travelling through -- vacuum, air, glass etc
out of those 3 it is fastest in a vacuum and slowest in glass
BUT in any given medium it is constant

robphy
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A better picture of a wave is a beaded string.

A bead along the string moves up and down ("transversely"). It does not travel down the string.
(For a longitudinal wave, the oscillation is along the direction of motion. However, the bead oscillates around the same center point of the string and does not travel far along the string.)

For light, the "Electric Field at that point" plays the role of the "transversally displaced bead".

What does travel down the string is the "disturbance" of that bead from its equilibrium position.
A bead further down the string will have the disturbance of its upward-neighbor.

The frequency of the oscillation of one bead (or of light at a point in space)
is different from the speed of propagation of the wave along the string.
They are related by the "wavelength" (marking the regular spacing of the disturbance-pattern in space).

Blue light has a shorter wavelength than red light.
Blue light has a higher frequency (shorter wave period) than red light.
However, the wave speed of light in vacuum is the same for both blue and red light.

We know the speed of light is a constant but speed is just the measure of distance over time. If blue light has a shorter wavelength than red but covers the same distance / time does this mean that blue light has actually made a longer journey than red light in order to arrive simultaneously?
Do you think that light will travel along the curved path of a sine wave, so under the same propagation distance, blue light will actually travel a longer distance than red light?
I think this is a misunderstanding. Light is a transverse wave. The amplitude of the sine wave only represents the amplitude of light. Light does not really travel along the curved path of a sine wave.

PeroK
robphy
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Do you think that light will travel along the curved path of a sine wave, so under the same propagation distance, blue light will actually travel a longer distance than red light?
I think this is a misunderstanding. Light is a transverse wave. The amplitude of the sine wave only represents the amplitude of light. Light does not really travel along the curved path of a sine wave.
I think the arrows in this diagram contribute to the misconception in the OP.
(There is no "winding road", as envisioned by the OP.)

That's why I think the "beaded string" I mentioned in the previous post is better in conveying
that it is
the disturbance of the bead at a point P--but not the bead itself---is what propagates along the axis.

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alan123hk and vanhees71
jbriggs444
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that needs to be qualified
The speed of light varies depending on the medium that the EM wave is travelling through -- vacuum, air, glass etc
out of those 3 it is fastest in a vacuum and slowest in glass
BUT in any given medium it is constant
To be pedantic, the speed of light in a medium is not necessarily a fixed constant independent of wavelength. Hence rainbows and prisms. For refractive index, I believe that it is specifically the phase velocity that is relevant. A quick trip to Google confirms.

nasu and vanhees71
Janus
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Think of it this way:
Light is like a train and the wave length is the length of each individual car. If the train travels at 10 m/s and each car is 10 m long, then the frequency at which cars pass is 1 car/sec.
If the cars are 5 m long, the same train speed produces a frequency of 2 cars/sec.
With light, the wave length is the distance between crests, and the frequency is how many crests pass per sec, with the light traveling at c.

gmax137
I do not like analogies, no I don't.

Take the beads on a string. This shows us that the wave is not the individual moving "things." OK. For a light "wave" what are the beads made of? How about the string? What exactly is "waving?" These are natural questions with no meaningful answer in terms of the analogy.

Here's my favorite analogy, explaining how radio works:
who knows said:
You see, wire telegraph is a kind of a very, very long cat. You pull his tail in New York and his head is meowing in Los Angeles. Do you understand this? And radio operates exactly the same way: you send signals here, they receive them there. The only difference is that there is no cat.

analogdesign, vanhees71, nasu and 1 other person
robphy
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I do not like analogies, no I don't.

Take the beads on a string. This shows us that the wave is not the individual moving "things." OK. For a light "wave" what are the beads made of? How about the string? What exactly is "waving?" These are natural questions with no meaningful answer in terms of the analogy.

Here's my favorite analogy, explaining how radio works:
The beaded-string analogy describes a transverse wave along a real [massless] string.

To apply to light,
• the string represents a line of abstract geometrical points in space.
• the bead (which represents the displacement of something from equilibrium on the line at that point) represents the [tip of the] electric field [vector] at that point in space.
Each bead along the string corresponds to the electric field at that point of the line.
(The electric field is chosen by convention.)
[Since we know the electromagnetic wave is a special configuration of time-dependent electromagnetic fields, we can also visualize a different "bead" (along a different plane) corresponding to the magnetic field.... and yet another "bead" corresponding to the Poynting vector field.]

• the disturbance that propagates is the electric field's value at one point propagating to be the electric field's value at another point along that line [assuming a non-dispersive medium].
The propagation of this "configuration (spatial pattern) of electric and magnetic fields at an instant of time" is the result of the Ampere-Maxwell law and the Faraday law, as constrained by the Gauss laws.
Here is my visualization of an electromagnetic wave using Glowscript
https://trinket.io/library/trinkets/216f415a46

@louis_slicka

Simply put, a wave is a propagating dynamic disturbance (change from equilibrium). In the physical and mathematical models of waves, the traveling path of a wave does not include the amplitude and wavelength of its dynamic disturbance in any way.

In electromagnetic waves, this dynamic disturbance is a change in the strength of electric and magnetic fields, so it is more obvious that it has nothing to do with the propagation path length of the wave itself.

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