Why are light waves depicted as lines, circles, and sinusoids?

[Themberchaud]

TL;DR Summary

Confused by waves

I have been studying light waves and also just waves in general, and I'm extremely confused by how these waves are drawn and depicted in physics.

If you watch the following video, you'll see what I mean:

In this typical explanation of the Thomas Young experiment, you see first that light waves are just represented by a straight vertical line. Then when the light passes through the slits, it is represented as concentric circles. Finally, when explaining interference patterns, you see waves depicted as sinusoidal waves like those that we study in trigonometry.

Other examples include when you strike water with a pin, you get concentric circles. Or sound waves are depicted as both concentric circles and also depicted as sinusoidal in nature. I've never seen sound waves or water waves depicted as straight lines, but I'm sure you could do that too.

These 3 completely different physical depiction of waves as lines, circles, and sines leave you wondering exactly what is a wave.

Can someone explain? Thank you for the help.

 

[PeroK]

A light wave is fundamentally an electromagnetic wave of oscillating electric and magnetic fields. The oscillating fields are at right angles to each other and to the direction of propagation.

Different sources produce different overall beams of light waves. A light bulb sends waves fairly uniformly in all directions. So, you might represent that as concentric circles. A torch or car highlights tend to focus the beam in one direction, which could be represented as a straight line.

If a light source is far enough away, then the waves become essentially a plane wave, which is a broad beam of light waves all travelling in the same direction. This is how Eratosthenes first measured the size of the Earth, by treating light from the Sun as a plane wave.

 

[Drakkith]

The problem is that light is a wave, but the only waves we are familiar with seeing are gravity waves (waves on the surface of water, not gravitational waves that we use long laser-based detectors to detect). Gravity waves have a sinusoidal motion that is easily seen and are so common that people will try to map this up and down picture to virtually every wave they learn of.

Light is a transverse wave, just like a gravity wave is. That means that the direction of the oscillation is perpendicular to the direction of the wave's motion. This is in contrast to a longitudinal wave where the oscillation is parallel to the direction of motion, such as in a sound wave. So many visualizations of gravity waves have analogous forms in EM waves (light).

Now imagine you drop a pebble into a pond and you get a bunch of concentric ring-shaped waves around the center. Pick one ring and draw a line at the very top (or bottom) and you'll get a circle. Do this for every peak and you'll get a bunch of rings which will expand outwards as time passes. This is the circle depiction, and we can often draw only part of a circle, an arc, after a wave passes through a tiny slit or other aperture.

Next, go back to that example of concentric waves moving out from the spot where we dropped the pebble. If we draw a bunch of lines perpendicular to the waves we will get straight lines coming out of the center and moving outwards, each line perpendicular to each wave crest or trough. This line is called a ray. It represents the direction the wave is traveling and is very convenient when we only want to show where a wave is going or simply don't care about all the waviness.

The sine wave depiction is usually used in two contexts:
1. To illustrate something about the wave. The water height for a gravity wave, or the field vectors for an EM wave.

2. A simple diagram where you draw a couple of squiggly lines to represent light. The squiggles don't actually represent something deeper. They are just using point 1 to make it very easy to immediately tell that the lines are light since light is a wave. Quicker and easier than drawing straight lines and then some text nearby that says, "LIGHT", or something.

 

[vanhees71]

A light wave is fundamentally an electromagnetic wave of oscillating electric and magnetic fields. The oscillating fields are at right angles to each other and to the direction of propagation.

This is a plane wave. For a wave at definite frequency it's
$$\vec{E}(t,\vec{x})=\vec{E}_0 \cos(\vec{k} \cdot \vec{x}-\omega t), \quad \vec{B}(t,\vec{x})=\vec{B}_0 \cos(\vec{k} \cdot \vec{x}-\omega t).$$
If you plug this into the Maxwell equations, it'll tell you that $\vec{E}_0 \cdot \vec{B}_0=0$, i.e., electric and magnetic fields are perpendicular to each other. Also you must have $\vec{k} \cdot \vec{E}_0=\vec{k} \cdot \vec{B}_0=0$, i.e., both fields are also perpendicular to the direction of wave propatation, and $\vec{E}_0$, $\vec{B}_0$, and $\vec{k}$ build a right-handed triple of mutually orthogonal vectors.

 

[Themberchaud]

A light wave is fundamentally an electromagnetic wave of oscillating electric and magnetic fields. The oscillating fields are at right angles to each other and to the direction of propagation.

Different sources produce different overall beams of light waves. A light bulb sends waves fairly uniformly in all directions. So, you might represent that as concentric circles. A torch or car highlights tend to focus the beam in one direction, which could be represented as a straight line.

If a light source is far enough away, then the waves become essentially a plane wave, which is a broad beam of light waves all travelling in the same direction. This is how Eratosthenes first measured the size of the Earth, by treating light from the Sun as a plane wave.

Okay, you explained how the light source itself can determine whether the overall beam of light is shown as concentric circle or a straight line in shape.

But I still am trying to understand exactly what sinusoidal depictions mean.

Drakkith says that the oscillation is either perpendicular or parallel to the direction of the waves motion.

So would it be fair to say that the lines or circles are just a rough depiction of the accumulation of multiple rays, but that the actual physical and real shape of a single light ray is an actual trigonometric wave?

In other words, if you had some sort of device that could show individual light rays, the rays would physically have peaks and troughs and periods and frequencies, and therefore a sine wave is what one ray of light really physically looks like.

Hope this makes sense, thanks for the help.

 

[Ibix]

So would it be fair to say that the lines or circles are just a rough depiction of the accumulation of multiple rays, but that the actual physical and real shape of a single light ray is an actual trigonometric wave?

It would be fair to say that there is no accurate drawing of an electromagnetic wave. All pictures are illustrating one aspect or another and will usually (depending on what you are reading) be honest depictions - just not accurate.

So when you see straight lines perpendicular to the direction of motion, or concentric rings coming from a point, they are marking the locations of amplitude peaks. This kind of diagram shows you the general shape in which energy is propagating. You can do the same thing with ray diagrams where you draw lines parallel to the propagation direction, but there's additional information about wavelength in the wavefront diagrams that may be important.

A third kind of diagram shows light as a sine wave, often with a row of arrows pointing to the wave from a central axis. Again this is an honest representation of a wave, but it's potentially very misleading. The problem is that the directions drawn perpendicular to the direction if travel are not representing space at all. They're representing electric and/or magnetic field strength. The field strength does indeed vary sinusoidally in the direction of motion - but this does not mean anything is being displaced to the side. So take a look at this diagram from Wikipedia:

(Credit: SuperManu). The axes should not be labelled $x$ and $y$ without further explanation. A much better labelling would be $E_x$ and $E_y$, with a second set of axes labelled $B_x$ and $B_y$ because they are plotting components of the electromagnetic field at locations along the one dimensional $z$ axis. There's no little bits of electromagnetic field being pushed up and down and left and right. Just varying (vector) field strengths.

 

[Drakkith]

So would it be fair to say that the lines or circles are just a rough depiction of the accumulation of multiple rays, but that the actual physical and real shape of a single light ray is an actual trigonometric wave?

A ray isn't real. It's a straight line we draw that's perpendicular to the direction of travel of the wave. The circles don't exist either. They're just marks on a piece of paper or pixels on a screen. The wavefronts that the circles represent are real, but both rays and circles are used to represent something that can't be seen. That is, you can 'see' light in the sense that your eye detects it, but you can't see how it moves or any of its properties. You can't see the EM field oscillate back and forth at each point in space. You can't see the interference of different waves that pass through the same space. You can't see the wavefronts as they spread out from a source. All of these things are invisible and can only be observed with specialized instruments.

Not only can you not see these things, the 3D space-filling nature of EM waves means that even if you somehow could see them, it would be an overlapping mess of nonsense. Illustrations, diagrams, and drawings have to simplify things for you to make any sense of them. Hence we use rays, circles, and squiggly lines to represent certain aspects of light and other EM waves.

 

[PeroK]

Okay, you explained how the light source itself can determine whether the overall beam of light is shown as concentric circle or a straight line in shape.

But I still am trying to understand exactly what sinusoidal depictions mean.

Drakkith says that the oscillation is either perpendicular or parallel to the direction of the waves motion.

So would it be fair to say that the lines or circles are just a rough depiction of the accumulation of multiple rays, but that the actual physical and real shape of a single light ray is an actual trigonometric wave?

In other words, if you had some sort of device that could show individual light rays, the rays would physically have peaks and troughs and periods and frequencies, and therefore a sine wave is what one ray of light really physically looks like.

Hope this makes sense, thanks for the help.

An electromagnetic wave comprises oscillating sinusoidal, electric and magnetic fields. Perpendicular to each other and the direction of propagation. See the diagram in post #6.

 

[sophiecentaur]

In other words, if you had some sort of device that could show individual light rays, the rays would physically have peaks and troughs and periods and frequencies, and therefore a sine wave is what one ray of light really physically looks like.

In real life we come across effects that can be explained in terms of rays or in terms of waves, depending on the circumstances. There is no such 'device'.
The rays that you see on diagrams are idealised depictions of what happens to the light. What you see when observing light can be explained in terms of rays there because of the wavelengths of visible light and the sizes of objects and holes in the world around us. A beam of sunlight from a keyhole will form the shape of the hole on a wall. This shape becomes bigger and more blurred as the distance increases. A simple 'explanation' of this is that the keyhole is big enough to allow a number of different 'rays' from all over an object top pass through it and the Sun has a finite angular size (about half a degree). The edges get fuzzy just by the geometry.

But small enough holes will reveal the wavelike nature of light to produce diffraction effects. A hole of around 1mm will not produce a sharp ray but a 'cone' of light that gets broader as the hole gets smaller' So you don't tend to get identifiable rays of long wave radio signals. Despite the old Scientists rule that Light travels in straight lines does not always apply; it can travel round the edges of objects and 'go round corners'.

 

[vanhees71]

An electromagnetic wave comprises oscillating sinusoidal, electric and magnetic fields. Perpendicular to each other and the direction of propagation. See the diagram in post #6.

These are pretty special solutions of the Maxwell equations, called plane waves. They don't exist in nature, because their creation would need an infinite energy. You can get all physical solutions by "superposition" of such plane waves (Fourier decomposision).

 

[Themberchaud]

Thanks for the responses, I will need to read this thread a few times to try and understand it.

I still am wondering exactly how do we know that the oscilliation is parallel or perpendicular to the direction of the motion of the photon.

If we can't see the ray and we can only measure the amplitude, how would you know the alignment of the wave in physical space?

 

[Drakkith]

I still am wondering exactly how do we know that the oscilliation is parallel or perpendicular to the direction of the motion of the photon.

If we can't see the ray and we can only measure the amplitude, how would you know the alignment of the wave in physical space?

1. We can directly measure the field vectors (the things that oscillate in an EM wave) at microwave and radio wave frequencies. It is trivial to set up an antenna and o-scope and move it around to take measurements at different positions around a transmitter.

2. The behavior of higher frequencies is identical to that of lower frequencies, so everything we measure from the latter still apply to the former.

 

[A.T.]

Okay, you explained how the light source itself can determine whether the overall beam of light is shown as concentric circle or a straight line in shape.

But I still am trying to understand exactly what sinusoidal depictions mean.

Drakkith says that the oscillation is either perpendicular or parallel to the direction of the waves motion.

So would
In other words, if you had some sort of device that could show individual light rays, the rays would physically have peaks and troughs and periods and frequencies, and therefore a sine wave is what one ray of light really physically looks like.

The circles are wavefronts, and the rays are their propagation direction, perpendicular to them.

The clean sinusoidal graphs apply only to monochromatic polarized light. Most light you see is just a chaotic waveform, just like with most sound you hear.

 

[PeroK]

I still am wondering exactly how do we know that the oscilliation is parallel or perpendicular to the direction of the motion of the photon.

James Clerk Maxwell first worked in out in 1865. Or, you could consult any modern textbook or lecture noteson Electromagnetism. E.g.
https://farside.ph.utexas.edu/teaching/jk1/Electromagnetism/index.html

In general, this is what's called mathematical physics.

I think Heinrich Hertz was the first to confirm Maxwell's work experimentally.

 

[Ibix]

we can only measure the amplitude,

You can measure amplitude and direction, and you can easily see which way EM radiation is travelling. Also you can polarise EM radiation, which isn't a concept that makes sense for longitudinal waves.

 

[sophiecentaur]

Thanks for the responses, I will need to read this thread a few times to try and understand it.

I still am wondering exactly how do we know that the oscilliation is parallel or perpendicular to the direction of the motion of the photon.

If we can't see the ray and we can only measure the amplitude, how would you know the alignment of the wave in physical space?

There is no way in which a single thread on PF can give you the grounding to enable you to leap into EM theory at this level without doing all the ground work. The World Wide Web and Wiki may give the impression that it's all pretty straightforward but there are too many factors for a simple solution.

 

[Themberchaud]

Yeah, I am getting the sense that this is far more complicated then I can understand at my level. I have a very basic high school level understanding of physics, if at all.

Believe it or not, Maxwell's equations make more sense to me on purely a mathematical level then understanding what a wave actually is in reality.

I want to re-read the answers you gave and think about them before I ask anymore questions in this particular thread.

Thank you for all your help.

 

[Mister T]

I still am wondering exactly how do we know that the oscilliation is parallel or perpendicular to the direction of the motion of the photon.

By oscillation I assume you mean the oscillation associated with the electromagnetic wave. But you cannot display wave properties like oscillation with a single photon. You need lots and lots of photons to observe the electromagnetic wave properties.

If we can't see the ray and we can only measure the amplitude, how would you know the alignment of the wave in physical space?

If you can measure the amplitude then you can measure the strength of the wave. Find the direction in which the strength is a maximum, that is the place where it's the amplitude, and you now know the alignment of the wave.

 

[sophiecentaur]

Maxwell's equations make more sense to me on purely a mathematical level then understanding what a wave actually is in reality.

You have a healthy respect for straightforward Maths )Maxwell) and the Maths of waves predicts / explains the transfer of energy; can't that be enough for you? "in reality" is not a valid term. Science doesn't try to answer the 'why' question or 'what things really are'.

Scratch the surface and our 'understanding' of things is little more than the amount that we can combine a number of already familiar models or ideas and come up with a satisfactorily believable new model which will become familiar eventually. Can't usually be done without Maths but you seem to have come to terms with that.