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Without any equations or complex terminology, I simply want to understand in complete layman's terms what the significance of a single photon's wavelength is. People say that microwave radiation's wavelength is as large as a baseball, and that a radio wave's wavelength is as large as the statue of liberty, but what does that even mean?

The photon is not literally going up and down constantly, photon's go on an almost straight path always, in a vacuum at least. What is the significance of saying that the wavelength is higher or lower, other than that a higher wavelength is less energy and lower is more energy? What are the legitimate physical characteristics measured that distinguishes all of these different sections of wavelengths apart from one another?

Qmechanic
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Neil Graham
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Wavelength is used as a convenience. It's much easier to imagine a photon with a 500 nm wavelength than to comprehend a photon oscillating 600 trillion times per second. But in reality that's all it is is a photon moving at the speed of light and oscillating 600 trillion times per second as it goes along. The photon completes one cycle every 500 nm. Many on this site do not agree with The idea of single photons so I'm sure this will be down voted but it does agree with experiment. The idea of a wave can only be explained with billions of coherent photons. Looking at photons this way it is easier to see why higher frequency photons have more energy.

Bill Alsept
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When these terms are used, light is been pictured as an electro-magnetic wave.

Thinking of the microwave example, inside what you would have is like a sea where light is equivalent to the undulations. So in this picture, the wave-length is the distance between two consecutive wave peaks. Larger wave-length implies more separation between these peaks.

Also the relation between wave-length and energy is also very similar to the sea picture. Large wavelength implies the "push" you get from several waves takes is more spaced, hence you receive less total energy per time interval.

On the contrary when the wave-length is shorter, you receive the "pushes" more frequently, i.e. they are less distanced from each other, and coming one after the other more rapidly, and the transfer of energy is higher.

Finally, to clarify the classical view of light: it is an electro-magnetic wave, that is a self-sustained oscillation in space an time of electrical and magnetic fields, each of them generating the other and propagating freely through both media and vacuum.

Clarification from comments:

The concept of light as EM waves is not reconcilable with the concept of photons. Those are two views of light which are incompatible. If you are trying to understand what light is, well in short we cannot explain it in layman terms so far. We can say that in some phenomena can be explained using the photon description but not the wave description, and others the opposite, while some can be explained by both. We have equations which gives us a complete explanation of these phenomena, but explaining them in layman terms is not easy, because in these equations light is neither photon nor wave, is just a physical entity which follows this equations but for which we don't have a simple conception, not as simple as photon or wave conceptions are.

rmhleo
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I'll guess that the most significant thing about the wavelength of light to the average person is simply the colors we visualize. Interestingly, the typical three types of cones in the human retina lose all information about frequency once the "photon" is detected. Thus, for a stream of photons all of one particular frequency, we detect three analog signals each at three different intensity levels. One type of cone detects what we call red, one type green, and one type blue. In order to make sense of those three inputs, the human brain sorts them out through the creation of color, so we see millions of colors from the relative strengths of just three electrical signals, as they vary in intensity. Color is a creation of the human mind, a psychophysical reaction to the three stimulae. It only exists in our minds. Here's a very short TED video I found on the subject, although the author fails to mention that all information about frequency is lost once a photon is detected by a cone. The "green" cones, for example, can detect a wide range of visible photons, but are more likely to be triggered somewhere in the center of the visual range, rather than at the ends, where a different type of cone is more likely to react to the photon. It's too bad he didn't show the overlapping cone sensitivities in the video. It's that overlap and the resultant changes in the amplitude of the three analog signals, that the brain sorts out into minor color changes. Pretty amazing - millions of colors from three signals. http://ed.ted.com/lessons/how-we-see-color-colm-kelleher