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## 1. Light

According to classical theories, particles and waves are two fundamentally different things. A wave has a wavelength and no well-defined location, and when different waves meet then they form interference patterns but keep going as if nothing happened. A particle does have a very well-defined position and no wavelength, and when different particles meet then they collide. Classical optics treats light and other electromagnetic waves as a wave phenomenon, and classical mechanics treats mass as made up of particles. The tacit assumption is that light is a wave phenomenon and therefore does not consist of separate particles, and that mass is made up of separate particles and therefore cannot show wave phenomena such as interference.

At the beginning of the 20th century it was discovered (through research by many people, including Albert Einstein) that this view is too simple, and that all things sometimes act as particles, and sometimes show wave phenomena. Light acts in some circumstances (such as in a solar cell) as a stream of separate particles which we now call photons, and particles such as electrons can under certain circumstances give interference patterns. In general, the particle characteristics of wave phenomena and the wave characteristics of particles are only important when you look at very small length scales, about as small as the wavelength or even smaller. At the by comparison very much greater length scales of daily life, the particle nature of light and the wave nature of particles are not important. These things are described by quantum mechanics.

At the very smallest length scales, all things have characteristics of particles. At those length scales, there turn out to be only a limited number of different kinds of particles, which are called elementary particles. A few of the better-known kinds of elementary particles are protons, neutrons, and electrons (which together form atoms and hence matter), photons (electromagnetic waves), neutrinos (of which there are at least three kinds), and gravitons (gravity waves). Protons and neutrons are made up of even smaller particles called quarks, but those cannot be found on their own.

Whether a group of similar elementary particles behaves at the length scales of daily life like a group of particles or like a wave depends on to which of two fundamental classes of elementary particles they belong. These two fundamental classes are called bosons and fermions, after Mr. Bose and Mr. Fermi who made important discoveries in this area. Protons, neutrons, electrons, and neutrinos are fermions, and photons and gravitons are bosons.

Bosons (such as photons) do not notice each other and can be at the same location at the same time without any problem. That's why different rays of light can cross each other without any problem and continue to go straight ahead as if nothing happened. Because bosons do not notice each other, it is very difficult to build a stable structure out of bosons.

Fermions (such as protons, neutrons, and electrons) do notice each other and cannot be at the same place at the same time. (Quantum fysicists say that different fermions cannot be in the same quantum state.) That's why two material things cannot just move through one another.

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## 2. The (Un)personality of Photons

People have many characteristics by which you can tell the difference between them. Even identical twins can be told apart if you study them carefully enough, for example by individual hairs or scars or individual cells in their bodies. At that level, there are many differences. Describing a person completely so that an exact copy could be made to the smallest level would require a truly staggering amount of information, more than would fit in all the computers in the whole world. It is therefore no problem to ascribe a different personality to each human.

Photons, however, have only very few characteristics by which they may be distinguished from one another. They have a not quite fixed amount of energy, an uncertain location, and a not quite fixed direction, and no other characteristics at all in which they differ from each other. The vagueness of the energy, location, and direction are quantum mechanical effects that are only noticeable for very small things.

For humans, their location and direction is usually not seen as part of their personality, and if you treat photons the same, then only their energy is left as part of their personality, and even the value of that quantity is somewhat uncertain. All in all, it is not easy to ascribe an individual personality to a photon. If two photons with about the same energy at about the same location go in about the same direction, and if we measure one of those photons a little while later, then we cannot be sure which of the two we measured. Also, you can see a photon only once, when you measure it, and that measurement changes the photon, because you can only notice the photon if it changes something in your detector, and that must (through Newton's Law that for each action there is a reaction in the opposite direction) affect the photon itself. So, you cannot keep track of a photon all the time, and that makes it even more difficult to establish the identity of a photon.

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## 3. Seeing Photons

Light consists of individual photons. A given photon can be seen by just one observer, because to be able to notice the photon a change must occur inside the eye of the observer, and that can only happen when the photon is absorbed by a light-sensitive cell in the retina in the eye. The observation of the photon makes the photon disappear. I think I read somewhere that a light-sensitive cell in the human eye needs at least about a dozen photons to arrive within a fraction of a second for the light to be noticed, so we cannot see individual photons. We can build instruments that can see individual photons.

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## 4. Are Photons Real?

The question whether photons are a theoretical device or reality is a philosophical question. How do you define the difference between a theoretical device and reality?

It is reasonable to assume the reality of photons because certain measurable things in the Universe can be accurately predicted from the assumed characteristics of photons. This suffices, and the reality of other things, such as atoms and cars and people, can be shown to be reasonable in the same way.

It is of course not a coincidence that photons seem to fit so well in reality; that is because the characteristics of photons were deduced from measurements of reality.

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## 5. The Weight of Light

Einstein found that mass can be transformed into energy, and energy into mass. Gravity sees no difference between mass and energy, so something can feel gravity because it has mass or because it has energy, or both.

If something goes faster, then it has more energy, which corresponds to more mass, so you could say that the mass of something has two parts: one that is due to the extra energy that the thing has (such as energy of speed [kinetic energy] or heat − there are still more of them), and one that remains if you remove all of the extra energy (which means that the thing doesn't move at all and is as cold as it can be). That last part of the mass is called the rest mass: the mass that the thing would have if it were completely at rest. The rest mass does not depend on the state of the thing (on its speed or temperature, for example). For example, the rest mass of all electrons is the same, so you can put that in a table in a book. The "mass-with-all-energy-taken-into-account" is different for each electron, and can be different from one moment to the next, so you cannot put that one in a table in a book. If physicists or astronomers talk about mass, then they usually mean the rest mass.

It turns out that matter has (non-zero) rest mass, but light does not. If you take all extra energy out of light, then nothing at all remains. When you ask a physicist or astronomer if light has mass, then they can answer "no" if they mean rest mass, or "yes" if they take the extra energy into account.

Light and matter are the same in some respects (for example, both of them notice gravity), but are different in other respects. For example, light can easily travel through a piece of glass without bothering the glass, but matter cannot do that. So, it is still useful (even for scientists) to distinguish between light and matter.

Things such as light that have no rest mass cannot be put on a scale to be weighed, so they have no weight (but they do have mass, if you take the energy into account). Mass and weight are not the same. You don't feel weight when you're floating freely in space, but you then still have mass, otherwise the force of gravity would not keep pulling you down and/or keep changing the direction of your movement.

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## 6. Changing the Direction of Light

The direction of light can be changed in different ways:

reflection

When light is reflected then you can usually predict the new direction pretty well. If the reflection is off of a smooth object, then you can predict exactly what the new direction of the light will be. Light can reflect from any object.

scattering

If light is scattered, then you can predict the new direction of the light only poorly or not at all. Scattering of light is usually done by very small particles, such as molecules of air (which make the sky appear blue), or dust particles, or very small drops of water in the air. The Moon during a total lunar eclipse is yet illuminated a little by sunlight that is scattered towards the Moon by the atmosphere of the Earth.

deflection

If parallel rays of light are deflected, then they are still (almost) parallel after the deflection, so their direction has changed in about the same way. Light can be deflected if the index of refraction of the medium through which it travels varies slowly. Light can also be deflected by gravity. See below for more information about this.

refraction

If light is refracted, then its direction changes suddenly, for example because it travels through an interface into a medium with a different index of refraction. Parallel rays of light usually remain almost parallel after refraction.

The difference between reflection and scattering of light is not always easy to determine. The difference between refraction and deflection of light is also not easy to specify. If the deflection takes little time, then it looks just like refraction.

If a ray of light passes close to a massive object, then it is deflected slightly by the gravity of that object. If the deflection is small, then it is approximately equal to $$φ$$ degrees:

$$φ ≈ 720 \frac{G M}{π c^2 r}$$

where $$G$$ is the Universal Constant of Gravitation, $$M$$ the mass of the object that the ray passes, $$c$$ the speed of light, and $$r$$ the shortest distance of the ray of light from the center of the object. If you measure $$M$$ in units of the mass of the Sun, and $$r$$ in kilometers, then $$φ ≈ 338.5/r$$. If you measure $$M$$ in units of the mass of the Earth, and $$r$$ in kilometers, then $$φ ≈ 0.001/r$$. The greatest deflection that a ray of light gets if it brushes past the Sun is 1.75 seconds of arc, and if it passes close to the Earth 0.0006 seconds of arc. These are very small deflections.

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## 7. Light at the Absolute Zero Point of Temperature

The only alternatives to reflection of photons are absorption of photons and the transmission of photons (i.e., being transparent). I haven't heard that supercold materials become transparent, so I assume that supercold materials (with a temperature close to the absolute zero point) absorb and reflect photons just like warm materials, so that supercold things can be visible against a suitable background with a different color or brightness.

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If you are somewhere where everything has the same temperature and there is no light from outside, then the surroundings are filled with (heat) radiation (including visible light) that appears equally strong from all directions, so then you can't see anything because there are no differences in color or brightness anymore.

So, you can only see contrasts if there are large temperature differences between the sources of light in your surroundings. Sunlight is sent into space at a temperature of about 6000 kelvin (degrees above absolute zero), which is much higher than the typical temperature in our environment (which is about 290 kelvin), and that is why things on Earth that the Sun shines on can show so much contrast (in color or brightness).

The heat radiation that things emit depends on the things' temperature. The higher the temperature is, the higher the average frequency (and lower the wavelength) of the radiation. We are much colder than stars, so we emit heat radiation at a much greater wavelength than stars, namely infrared radiation instead of visible light.

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## 8. Light in Space

You only see the light that reaches your eyes, just like you only hear sounds that reach your ears or smell smells that reach your nose. In this regard, all senses are equal. Light in space behaves just like light on Earth, so in space, too, you only see an object if it emits or reflects light into your eyes. If no light falls on an object and if it does not emit light of its own, then that object is invisible to everybody.

Only those parts of the Earth or of a spacecraft that are lit are visible. If the Earth moves between the spacecraft and the Sun, then the spacecraft moves through the shadow of the Earth where it is night. Then, no sunlight reaches the spacecraft and it is dark (except where lamps burn in or on the spacecraft). From the spacecraft, you can then only see things on Earth that emit light themselves, such as city lights or gas flares on oil rigs. If the spacecraft gets close to the boundary between day and night again, then you can see a little sunlight at the edge of the Earth that is refracted by the atmosphere of the Earth, just like from the ground you can see the sky brightnening some time before sunrise and it doesn't get completely dark until some time after sunset.

The landings on the Moon were always done in places where it was daytime then, so the Sun shone down on those sites and the ground looked bright in photographs that the astronauts took.

So, it is not always dark when you're in space, because the Sun always shines. The Sun is hidden from your view only if you're in the shadow of a planet or moon or asteroid. The space probes that we send to the Moon or to the other planets are in sunshine for the whole trip, until they go into orbit around the Moon or the planet. When they're in orbit, then they can go into the shadow of the Moon or planet once in a while, and then they are in darkness.

If you're in deep space between the stars, then it is about as dark as it is on Earth in the middle of a clear night far away from city lights. You can then see all of the stars, so it is not completely dark, but all of the light from all of the stars put together is not enough to read a book by.

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## 9. The Aether

Scientists noticed in the 17th century that light has properties of a wave phenomenon. All other wave phenomena that they knew, such as water waves and sound waves, require a physical medium to travel through. Surely, something had to do the waving. For example, there are no water waves without water, and sound does not travel through the vacuum of empty space (so all movies in which you can hear a space ships travel through space are wrong). People therefore assumed that light also needs a medium to travel through, and that medium had to fill the whole Universe (because we can see the planets and stars) and but it could not give any friction (because otherwise the planets would have ground to a halt long ago because of the head wind from the medium). People started searching for proof of the unknown medium, which they called the aether.

The search for the aether turned out to be fruitless. Whatever was tried to catch the aether in some experiment, nothing provide convincing proof that the aether exists. The best-known of the experiments was the one by Michelson and Morley in 1887, who tried to very accurately detect the motion of the Earth relative to the aether, but found no trace of it. Many more of these kinds of experiments have been tried.

So, there are no indications that our current understanding of light (without an aether) is incomplete. If there were an aether with measurable influence on light, then you'd expect that our measurements of light would show unexplained deviations compared with our theory of light, which does not include the aether, but there are no such deviations. Of course, it is always possible that there are as yet unknown kinds of particles or other things in the Universe, but if there is yet a kind of undiscovered aether that fills the whole Universe, then it apparently has no influence on light, so it would not be the aether that people had been looking for for so long.

For more information about the search for the aether and about the Michelson-Morley experiment, you can go to //galileoandeinstein.physics.virginia.edu/lectures/michelson.html.

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## 10. Scattering of Light

Light that meets obstacles will be reflected or scattered by them. That means that part of the light is sent into different directions. And that is a good thing, because otherwise we could only see things that emit light of their own, such as the Sun and fire and lamps, but not the ground or a tree or a wall. If the light changes direction in the same way across a large area, then we call it refraction or reflection of light. If the light goes randomly in all kinds of directions, then we call it scattering of light.

How well scattering works depends on the size of the obstacles (particles) and on the wavelength of the light.

A cloud in the sky is made up of very many droplets of water, which are really small but yet much greater than the wavelength of the light. In such a case, all wavelengths (colors) are scattered equally well, and that's why such a cloud looks white.

Fog is like a cloud that lies on the ground, so it is also made up of very many very tiny drops of water. If you stand in a fog at night near a street light or lamp, then it seems as if part of the light doesn't come from the lamp but from the fog around the lamp. That light did in fact come from the lamp and was on its way in a direction very different from that towards your eye, but then bumped into a fog droplet and was redirected towards your eye after all. Because your eye can only see where the light came from last, it looks as if the light didn't come from the lamp but fromt the fog droplet instead.

If the diameter of the scattering particles is less than about one tenth of the wavelength of the light, then the scattering is much easier for smaller wavelengths than for longer wavelengths (namely, inversely proportional to the fourth power of the wavelength). This kind of scattering is called Rayleigh scattering, after mister Rayleigh who explained it. Blue light has a wavelength that is about half as large as that of red light, so blue light is scattered about 16 times easier than red light.

Atoms and gas molecules (like those in the air) and tiny dust and smoke particles are small enough that they can produce Rayleigh scattering of light. Part of each light ray that comes from the Sun and travels through the atmosphere is scattered, and this part is mainly the blue part. Blue will be lacking from light rays coming directly from the Sun to your eyes, because it was scattered into many different directions, so the Sun looks a bit yellow (because if you take away blue from white light then you get yellow). Of light rays that pass you by, some blue light is scattered in all directions, and also towards your eyes, and that light does not seem to come from the Sun but rather from the air molecules that scattered it towards you. That's why the sky looks blue.

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## 11. The Speed of Light

In empty space (a vacuum), light (and other kinds of electromagnetic radiation) always travels at the same speed, which is therefore usually called the speed of light. That speed of light is by definition exactly equal to 299,792,458 m/s and is usually written $$c$$ in formulas. In terms of miles, this is equal to 186,283 miles per second (rounded to the nearest whole number).

We do not know why light should travel through a vacuum at a constant speed, so you could say that we don't fully understand light yet. But how can you prove to someone else that you completely understand something, even if that other person would not understand your explanation of how it works? I think that the only way you can do that is to show that you can make correct predictions about the thing in all cases, because someone else can tell if your predictions come true, even if he doesn't understand where you get those predictions. However, we cannot possibly check all circumstances to make sure that our predictions are correct, so I do not think that we'll ever achieve ultimate understanding. But we can strive to get closer to it.

Our best models of how everything works still contain many "free parameters", like knobs and dials that have to be set very carefully to specific values in order for everything to turn out as it is, but of which we do not know why precisely those values are necessary. One objective of modern science is to reduce the number of these free parameters, by uncovering hidden logical patterns that explain why certain free parameters are in fact tied together, so that a smaller number of free parameters is enough to explain everything. The ultimate goal is to find a Grand Unified Theory or Theory of Everything, which contains no free parameters at all anymore (but does predict everything accurately). Then all values that seem to exist independently, such as the mass of the proton or the diameter of a hydrogen atom or the speed of light in a vacuum or the universal constant of gravity will turn out to be based entirely on dimensionless numbers such as pi and 4 and the square root of 2.

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The current value of the speed of light in a vacuum is set by definition, but was the result of a long series of measurements and calculations. Ole Rømer was the first, in the year 1676, to find a reasonable value for the speed of light (expressed as "22 minutes to cross the orbit of the Earth", but the "true" value is just below 17 minutes). Hyppolyte Fizeau was the first, in 1849, to measure the speed of light in a laboratory experiment (and found a value that was about 4 percent too high). After that, the measurements got increasingly more accurate.

## 12. Adding Speeds

In ordinary life, speeds add up. If Ann walks 1 km/h faster than Burt and Burt walks 2 km/h faster than Clara, then Ann goes 1 + 2 = 3 km/h faster than Clara. The same does not hold for light (and other kinds of electromagnetic radiation). If Ann, Burt, and Clara walk in the sunshine and measure the speed of the sunlight, then all three of them get the same result, even though they are not all walking equally fast.

If light travels not through empty space but rather through a gas (air) or a transparent fluid or solid, then the speed of the light in that substance is less than the speed of light in empty space. The ratio of the speed of light in empty space and the speed of light in a substance is equal to the index of refraction of that substance. The index of refraction of water is about 1.4 (depending on the color of the light), so the speed of light in water is equal to about $$c/1.4$$ which is about 0.7$$c$$, which is about 210,000,000 m/s or about 130,000 miles per second.

Here is the speed of light in a number of different units.

Table 1: Speed of Light in Various Units

value unit
1,079,252,849 km/h kilometers per hour
670,618,310 mph miles per hour
299,792,458 m/s metesr per second
299,792.458 km/s kilometers per second
186,282.864 mi/s miles per second
63,241.08 AE/y astronomical units per year
173.14 AE/d astronomical units per day
7.481 earth circumferences per second
7.214 AE/h astronomical units per hour
1 ly/y lightyears per year
0.3066 pc/y parsec per year
0.002004 AE/s astronomical units per second

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To know how long light takes to travel 900 km you need only divide that distance by the speed of light, which is (see above) almost 300,000 km/s. So, 900 km takes light only 900/300,000 = 0.003 seconds to travel (in empty space). 900 km is equivalent to about 560 mi, so you can also calculate the time as 560/186,283 = 0.003 seconds.

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Massless particles always travel at the speed of light, so they do not need to be accelerated to that speed. Light (photons) does not need to accelerate from zero to the speed of light, but goes at the speed of light right from the start. Other wave phenomena need no acceleration, either, but go at the appropriate wave speed right from the start.

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## 13. How Long Is A Lightyear?

A lightyear is the distance that light travels (through empty space) in one year. A lightyear is not a period, but a distance. The speed of light in empty space is a constant (see above), but one can argue about the length of a year, if you want to be very precise. We'll use the average Julian year of 365.25 days. With this, a lightyear is equal to $$299,792,458 × 60 × 60 × 24 × 365.25 = 9,460,730,472,580,800 \text{ m}$$ or about 9.5 million million kilometers or 5.9 million million miles.

The speed of light can also be combined with shorter units of time such as days and seconds. Here is a list.

Table 2: Lightyears and their Kin

unit length
lightsecond 299,792,458 m 186,283 mi
lightminute 17,987,547,480 m 11,176,972 mi
lighthour 1,079,252,848,800 m 670,618,310 mi
lightday 25,902,068,371,200 m 16,094,839,450 mi
lightyear 9,460,730,472,580,800 m 5,878,640,109,306 mi

## 14. Light Phenomena

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### 14.1. Halo

A halo is a circle of light (or part of such a circle) around the Sun or Moon. "Halo" is also used more generally to refer to any optical phenomenon involving the refraction of light by ice crystals. The most common kind of circular halo surrounds the source of light at a distance of about 22 degrees from the center of the source of light. The most common kind of optical phenomenon involving ice crystals (at least in my experience) are sundogs, which are patches of light (often with the colors of the rainbow in them) at about 22 degrees to the left or right of the Sun.

A halo is caused by sunlight or moonlight being refracted into your direction by small by ice crystals in the atmosphere. If you see a halo, then there must be small ice crystals in that direction in the atmosphere. The shape of the halo is determined by the orientation of the ice crystals in the air, and of course by the presence of ice crystals in the air. If there are no suitable ice crystals in the direction that is appropriate for a halo, then you won't see a halo in that direction.

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## 15. Brightness

Some people can say that the Moon is brighter than the stars, and other people can say that the stars are brighter than the Moon. Both groups can be right, because they mean different things by "brightness".

How do you tell if one thing is brighter than another thing? You might measure how much light reaches you from both things, and see which amount is larger. If you do that, then the Moon is brighter than all stars combined. Or you might measure how much light leaves both things (in all directions), and see which amount is larger. If you do that, then any star is much brighter than the Moon.

Seen from Earth, the stars look less bright than the Moon does because the stars are very much farther away from us than the Moon is. If you put the Moon as far away as the stars, then the Moon would be so dim that you couldn't see it anymore even with the best telescope.

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## 16. Is the Moon a Source of Light?

If you see a bright light in the sky, then you can't tell immediately whether that light was reflected or whether it came directly from the place where it was created, without any reflections along the way. So, there must be a way to refer to "a small part of the sky [all directions] from where light arrived here", and that is commonly called a source of light. If you want to discuss where that light was originally created, then you have to use more words.

This is similar to sources of other things. A "source of water" is a small area from where water flows, regardless of where that water originally came from. A "source of wisdom" is a person who says many wise things, even if some or all of those wise things were told to that person by someone else.

In common speech, moonlight is "light coming from the Moon", regardless of the ultimate source of that light. This is practical. It means that you can see the Moon, and that you have some light for your nightly activities. For those things it makes no difference whether the moonlight was created by the Moon or is actually reflected light from somewhere else, perhaps from the Sun.

It is entirely similar to the definition of sunlight as "light coming from the Sun". These definitions focus on the effects rather than the causes. You need such effects-based definitions before you can start thinking about the causes.

The first thing you do when you find yourself in unfamiliar surroundings is to give the important things names, so you can talk about them. After a while you start to understand how those things relate to each other, but that is no reason to throw away the names that you gave to them earlier. "Moonlight" is a name, not an explanation. Everybody recognizes moonlight when they see it, even if they don't have any clue about where that light was ultimately generated.

There is another definition of sunlight as "light that was generated by the Sun". That definition focuses on causes rather than effects. It depends on the situation which of those definitions (cause-based or effects-based) is the most appropriate. If the distinction is important to you in a particular situation, then you must clarify which definition you use.

It is not reasonable to insist that everybody use a cause-based definition unless you know what all of the causes are, and history shows that it is unwise to be too confident about the completeness of your knowledge.

If you insist on a cause-based definition, then the definition of moonlight as "light from the Sun reflected by the Moon" is incomplete. The Moon does in fact generate some visible light of its own, as all objects do that are above absolute zero temperature. The cause-based definition excludes that light generated by the Moon from the definition of moonlight, which seems silly.

Also, the Moon does not reflect just sunlight, but also starlight, which was certainly not generated by the Sun, so it should then be included in the definition of moonlight, too. If there were a second star nearby to rival the Sun, then its light would surely have been included in the cause-based definition of moonlight, so it seems illogical to define moonlight purely in terms of sunlight.

In addition, part of the moonlight is sunlight that was reflected more than once, but the above definition is not clear about whether such multiply-reflected sunlight is included. One example of such multiply-reflected sunlight is earthshine, which makes the dark part of the Moon facing the Earth visible within a few days from new moon.

And finally, the Moon is not merely a passive reflector of sunlight, but leaves its mark on the reflected light. It reflects certain colors better than others, so that a knowledgeable scientist can tell the difference between sunlight and moonlight by looking at the spectrum of the light.

I expect that most people are not aware of these different components of the light coming from the Moon (even if they know that most moonlight is reflected sunlight). And perhaps we'll discover a few more components as our knowledge of the Universe increases. Any cause-based definition may therefore turn out to be incomplete, but the effects-based definition remains valid.

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