How to study EM wave interactions via internet?

[brainstorm]

I would like to do some reading about how EM waves interact with each other via internet. Upon googling "EM wave interaction," I got some general links about EM radiation and some book titles but I didn't see any websites. Does anyone know one or more good online sources that give an overview of different kinds of EM wave interactions and an explanation of how the interactions work? BTW, I don't even know where to post this question on this forum because none of the physics sub-forums specifically mention EM radiation. Thanks.

 

[Born2bwire]

Electromagnetic waves follow linear superposition. They simply add up so you are not going to find much about how the waves interact with each other. It is how they interact with matter that is of primary interest.

 

[brainstorm]

Electromagnetic waves follow linear superposition. They simply add up so you are not going to find much about how the waves interact with each other. It is how they interact with matter that is of primary interest.

What adds up, exactly? The wavelength? The frequency? Why does red and green result in yellow, green and blue result in cyan, and red and blue result in magenta? The frequency of yellow is between red and green, as is cyan between green and blue, yet magenta is higher than both red and blue. Am I missing something very obvious here?

Also, is white light a single wave pattern or a multiplicity of simultaneous wave patterns? If it's a multiplicity, when do waves converge into a single hybrid waveform and when do they remain multiple? Again, I may be missing something obvious and/or fundamental.

 

[Born2bwire]

What adds up, exactly? The wavelength? The frequency? Why does red and green result in yellow, green and blue result in cyan, and red and blue result in magenta? The frequency of yellow is between red and green, as is cyan between green and blue, yet magenta is higher than both red and blue. Am I missing something very obvious here?

Also, is white light a single wave pattern or a multiplicity of simultaneous wave patterns? If it's a multiplicity, when do waves converge into a single hybrid waveform and when do they remain multiple? Again, I may be missing something obvious and/or fundamental.

The components of the waves just add up. If we have two electromagnetic waves and we describe the electric field component as say E_1(r,t) and E_2(r,t) then the resulting wave is simply E_1(r,t)+E_2(r,t).

Red and green does not result in yellow light. Red and green light is simply red+green light. Our eye only perceives around the three primary colors. Our brain takes in the eye's measurement of the three colors and interpolates the resulting colors across the entire visible light spectrum.

White light is all frequencies that fall in the visible light spectrum. It is a superposition of all colors.

 

[brainstorm]

The components of the waves just add up. If we have two electromagnetic waves and we describe the electric field component as say E_1(r,t) and E_2(r,t) then the resulting wave is simply E_1(r,t)+E_2(r,t).

Could you give an actual example of adding two different wavelengths and the third wavelength they add up to so I could see concretely what you mean? I don't get what the r and t stand for, for example.

Red and green does not result in yellow light. Red and green light is simply red+green light. Our eye only perceives around the three primary colors. Our brain takes in the eye's measurement of the three colors and interpolates the resulting colors across the entire visible light spectrum.

So the waves do not merge into a single hybrid wave? I read that two waves of the same wavelength can either double brightness or cancel each other out depending on whether the peaks line up together or the peaks with the troughs. I assumed this meant that the waves actually combine to increase or decrease each other's amplitude. Thus, I thought that if two waves of different lengths combine, the resulting wavelength would be some hybridization of the component waves.

White light is all frequencies that fall in the visible light spectrum. It is a superposition of all colors.

So white doesn't have a specific wavelength because if it did it would be some color instead of white? And the reason we see mixed colors is because of our brains making sense of more than one color at the same time, when in fact the frequencies remain separate and interact differently with different parts of the cornea/retina (or something like that)?

 

[Dr Lots-o'watts]

So the waves do not merge into a single hybrid wave? I read that two waves of the same wavelength can either double brightness or cancel each other out depending on whether the peaks line up together or the peaks with the troughs. I assumed this meant that the waves actually combine to increase or decrease each other's amplitude.

It's a simple summation of amplitudes E1 and E2. r and t are position and time.

Thus, I thought that if two waves of different lengths combine, the resulting wavelength would be some hybridization of the component waves.

No. If you tap the floor at 1 beat per second, and I tap the floor at 2 beats per second, we haven't combined our frequencies, we are still independent at 1Hz and 2Hz. What may combine is the force of our taps if they are simultaneous.

So white doesn't have a specific wavelength.

No. White is what our brain pictures when it receives every wavelength in the visible spectrum at roughly equal intensities.

EM wave interacting with each other is basically interference, you may want to start here : http://en.wikipedia.org/wiki/Interference_(wave_propagation)

 

[brainstorm]

It's a simple summation of amplitudes E1 and E2. r and t are position and time.

This is the idea I basically started with. I assumed if you would treat two EM wave beams as stationary, that when you combine them the waves would merge to form a new wave with the combined amplitude and some average frequency.

No. If you tap the floor at 1 beat per second, and I tap the floor at 2 beats per second, we haven't combined our frequencies, we are still independent at 1Hz and 2Hz. What may combine is the force of our taps if they are simultaneous.

That's a difficult analogy considering that there is no overlap except when every other 2bps tap matches with every 1bps tap. A better example might be if you play a C note with another C an octave higher, it doesn't create a beat/harmony, whereas if you play a C note with any other note, it does. So white light may actually be comparable to combining all notes between Cs in equal proportions?

No. White is what our brain pictures when it receives every wavelength in the visible spectrum at roughly equal intensities.

So what is the difference if you combine red, green, and blue to make white or all the colors together? Do you get different whites? Also, how do you know a particular frequency of red isn't 5 different waves of very similar frequency?

EM wave interacting with each other is basically interference, you may want to start here : http://en.wikipedia.org/wiki/Interference_(wave_propagation)

Thanks, this is interesting. What I am really interested in, though, is how the various forms of radiation outside the visible spectrum could combine and interact with each other.

 

[Dr Lots-o'watts]

... some average frequency.

No. There is no physical "average" frequency. There are still two, the same two as before.

So white light may actually be comparable to combining all notes between Cs in equal proportions?

Almost. This is how an LCD monitor produces white, with a few distinct frequencies that together fool our brain into thinking it's white. In this sense, our brain does an "average", but it's not a mathematical average in the common sense, it's "sensory", beyond the scope of physics and mostly neuropsychological IMO.

True white would be a continuous spectrum that would include the infinity of frequencies in the visible range. The analogous sound "white" would contain all frequencies between 20Hz and 20000Hz, it would be perceived as noise, perhaps the background noise in a city or in a crowd are examples.

So what is the difference if you combine red, green, and blue to make white or all the colors together? Do you get different whites? Also, how do you know a particular frequency of red isn't 5 different waves of very similar frequency?

You can get whites with a tint of each color, pale pink, blue pale, different shades etc. Look at a color chart where they sell paint. Or better go to the menu where you can set the colors of your computer screen. All these tints are made up of only a few wavelengths (I think it's 3 : RGB). A particular frequency of real-life red could very well be made up of 5 similar but distinct frequencies. But this doesn't change a thing in everyday life. Most of the colors we see are indeed a mix of many frequencies. While traveling they are superposed and distinct, but when the reach our eyes, the brain makes an "average" (non-mathematical) as you say.

Thanks, this is interesting. What I am really interested in, though, is how the various forms of radiation outside the visible spectrum could combine and interact with each other.

If you are only looking at waves, it's exactly the same physics for wavelengths. Interference is practically the only effect that can happen between two waves in the absence of matter. No matter how complex the equations can be, it's always just superposition.

Wavelength only matters in relation to matter. This however can give rise to a host of effects that are subdivided in the many fields of physics.

 

[brainstorm]

So why is it that red and green light combine to make yellow, whose frequency is between red and green. Green and blue combine as cyan, which is also in between the two. Yet red and blue combine to make magenta, which appears to be on the violet side of blue?

Is this just pure coincidence or does wavelength of the "ingredient" colors correlate in some way with the apparent color resulting from them mixing?

 

[jtbell]

Could you give an actual example of adding two different wavelengths and the third wavelength they add up to so I could see concretely what you mean?

See for example

http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html

You probably can find other examples by Googling for "wave superposition".

 

[brainstorm]

See for example

http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html

You probably can find other examples by Googling for "wave superposition".

Those are some very nice animations. The one about "beat" interactions was especially interesting because it dealt with two waves with the same velocity but different frequencies, which applies to EM radiation if EM waves in fact interact/superimpose in this way. I don't see why they wouldn't, because if two beams of the same frequency can result in interference patterns of amplification or dimming, depending on the phase, why wouldn't more complex interactions like "beats" occur?

My next question would involve whether the mixed-effect of two frequencies, such as red and blue resulting in magenta, could be due to the beat frequency resembling that of another wavelength. If this was the case, I would think you could combine various forms of EM radiation to generate beat frequencies that would simulate other wavelengths, such as combining microwaves with infrared to get UV or something like that. Maybe I should just put a plate of glowing coals in the microwave oven and see if I get a suntan (this is a joke, btw).

 

[individual61]

My next question would involve whether the mixed-effect of two frequencies, such as red and blue resulting in magenta, could be due to the beat frequency resembling that of another wavelength. If this was the case, I would think you could combine various forms of EM radiation to generate beat frequencies that would simulate other wavelengths, such as combining microwaves with infrared to get UV or something like that. Maybe I should just put a plate of glowing coals in the microwave oven and see if I get a suntan (this is a joke, btw).

That has nothing to do with why coloured light creates "new" colours when you look at two overlapping beams of different-coloured light.

For other wavelengths, however coherence plays a big part in why this is not feasible (Wikipedia has good articles on coherence length, for example).

With that said, this in fact does happen. I apologize for not explaining it myself, but if you were to look at the articles on parametric downconversion (http://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion ) you'll find an example. I realize that in that case, one photon results in two photons, and you are asking about the reverse process, but I believe the reverse process is also possible in that context. Anyone care to confirm?

d.