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A wave of light in the current of water

A wave of light in the current of water 

Light has the curious property that its direction is refracted when it passes obliquely from a denser medium into a more dilute one. The thinner medium is, properly speaking, optically speaking a thinner medium, and the denser medium is optically speaking a denser medium. Or the other way round, we call this refraction, which is actually a very trivial name. Therefore, we are not talking here about the density (specific gravity) of the medium, but about some deeper properties of the medium.
  We are talking about the sine of the angles of refraction entering and leaving the medium, but it is more illustrative to think in terms of the speed of light proportional to this. The index of refraction for vacuum is n0=1, for air nlev=1.003, for water nwater=1.33, and for diamond ngy=2.2. The numbers n show how many times slower light travels in the medium than in a vacuum. The basis for the conversion is the speed of light in a vacuum, which is a value calculated with high precision, c=299 792 458 meters/second. Thus, in water, the speed of light c/1.33= 225 407 263 m/s. So light travels slower in water than in a vacuum, but why?

When the water standing

  The inside of the water also hides many secrets. Think of a glass tube placed horizontally in a vacuum, filled with water, and sealed at the ends with transparent discs. Above and below the tube, and before and after it, the speed of the light waves is of course c. In the glass tube, the water is less than c, corrected to the water value cwater just calculated:       

0.) cwater=c/n.

The question is: does the density and height of the waves traveling slower in water change? Yes, it does, as shown in Figure 1.

Figure 1 Variation of light waves in water

    The tube is surrounded by very dense and very high-energy but completely transparent material called a vacuum.  Although it is completely invisible and colorless, it is marked in purple in the diagram. The vacuum penetrates inside the glass tube and even into the atoms of water. The atoms have the special property of absorbing energy intensively, using it to sustain themselves, and then sending it out unnoticed - perhaps into hyperspace. (See here for more!) In water, the energy of the vacuum decreases with a refractive index of n. This gives both its changed energy and its velocity using a multiplier of 1/n, or 1/1.33. The vacuum in the water, therefore, propels the light with reduced energy and reduced speed. The ratio of 1/1.33 reduces the length of the light wave and the height of the waves. The waves traveling in water are therefore proportional to the waves in the vacuum, but 1.33 times smaller.

  The obvious question is where the energy content of the larger wave goes when its size becomes smaller. It is lost, and the energy difference is absorbed by the water. And what happens when the smaller wave leaves the water and has to move on as a larger wave? What will happen is that the vacuum will immediately transfer enough energy to the light wave. The vacuum will not prevent a light wave of a given frequency from having a smaller wavelength, smaller amplitude, lower speed, and lower energy than its energy state dictates.     

The lengths of the arrows in the diagram show us the speed of the waves: the wave entering the vacuum will have a higher speed, the wave traveling through the water will have a lower speed, while the wave exiting the vacuum will again have a high speed. The local energy states are indicated by the size of the letters E. In the figure, local energies are denoted by the larger letter E, while the subscript 0 indicates the ground state of the energy. In water, the energy is smaller in proportion to the refractive index n, hence the Ewater notation is smaller.  

The findings of the above experiment are confirmed by everyday life when we look at a ray of light passing through a double-glazed window. The ray of sunlight is traveling through the air at a speed of nearly a vacuum. When it penetrates the outer glass plate, it slows down because the refractive index of the glass is close to the refractive index of water. After exiting, it accelerates again, slows again into the inner glass plate, and then accelerates again upon exiting. This repeated speed number can be further increased by adding more glass plates in the path of the light beam.

The refractive index of water and other transparent media is easy to measure using an inclined beam and a protractor. The optically denser medium is poured into a glass vessel, a beam of light is obliquely introduced, refracted on entry and the refractive index is calculated from the ratio of the angles. However, constructing such a device and moving the optically dense medium at high speeds is difficult, and not many such experiments have been carried out.

When water moves

The velocity w was measured with great accuracy by the experimental physicist Zeeman because he managed to move a glass cylinder at high speed. He fired the finely polished glass cylinder from a small cannon, so it is a slight exaggeration to say that the cylinder flew at the speed of a cannonball. Meanwhile, the split beam passed one branch of the light beam through the glass cylinder and sent the other branch past it, in the air, in the direction of the observation point.

Figure 2 The Zeeman experiment

Based on the different measurements, he established an empirical formula to calculate w: 

1) w=c/n + v/n2

 The formula is good, but it is not clear why it is the way it is. You could say that it's because only!   Or we could say that nature is just like that.

The derivation of the formula

In what follows, however, I will try to explore the physical content of the formula. We naturally assume that light passing through a moving glass cylinder is carried along by the medium, and so the light travels faster with the speed of the motion. This idea can be expressed in the formula:    

 2) w'=c/n +v

where w' is the changed velocity of light and v is the velocity of the glass cylinder.
However, this formula is not correct in this form. The above formula would be true only if the liquid, i.e. water, was not penetrated by the ether and had no significant effect on the moving light and the moving water atoms or atoms of the glass cylinder.

In terms of effect, water fills the glass cylinder only two-thirds full, because the stationary aether effect is also one-third full. As a consequence, the added velocity is not v but v/n. So the refractive index also enters in the second term of the formula, which reduces the light-speed velocity. What has been said so far in formula form looks like this:

3.) w''=c/n + v/n 

Figure 3 Theoretical presentation of the Zeeman experiment

   Figure 3 shows the Zeeman experiment again with a small change, but with an important theoretical addition. Of course, it only looks elongated for light because it has to travel a longer distance due to the speed v. This extra distance is seen in the nose (front) of the glass cylinder, as if the glass cylinder had been slightly elongated. If the light wave path is broken down into three phases, the first phase is the moment when the light wave reaches the cylinder from behind and starts to penetrate it. The second phase is when the light wave passes through the moving glass cylinder of length L. By the time the light wave reaches the front of the moving cylinder, it has already moved forward by DL. This implies extra distance and extra time compared to the vacuum motion. This must somehow appear in the formula, which can be created by multiplying the second term by another 1/n. This is a multiplication of 1/n2 in the second term of the final formula and thus further reduces the entrainment rate. This multiplication thus returns Zeeman's experimental result numbered 1:  

4) w=c/n + v/n2

It is clear that the theoretical formula quoted is the same as Zeeman's formula 1 derived by an experiment. My little optical derivation above does not, however, make me confident. Scientists of the time published many precise optical measurements, and there must be a few hefty volumes in some professional library where the above derivation is hidden. Perhaps I have the merit to refresh and reintroduce this currently out of circle rotation, but still a very valuable topic.

   If we think about it, Zeeman's formula No. 1 implies another physical effect besides the capture of light. It is that light leaves one optical system, the glass cylinder, and enters another medium, the vacuum. In the meantime, he also included a tricky medium switching step in the formula. Thus the basic entrainment formula (the correct formula) is formula 3: W"=c/n+v/n. There is, however, another type of such experiment where the light does not need to cross into another medium but can remain in the moving water and thus directly give the entrainment formula 3. One such experiment was that of the Frenchman Fizeau, where the light never left the water, it just went round and round.

As an afterword, let me say a few final thoughts on the above topic, or rather on the general nature of light. These are was certainly not covered in the well-developed German textbooks. One is that, in my opinion, we are still very much at the beginning of the journey of understanding light. The solution to the problem of light is still in children shoes. Science still has a lot to do, in terms of time and energy, to make the exit at the end of the dark tunnel clearer. And it is a long way off before a beautiful palace of light is finally built. I myself, with 3 bricks, tried to contribute to the construction: see more here, here, and here! I think this is still a sweet understatement, so I'll make an attempt to summarise and publish my own additional thoughts and opinions so far. There are still many steps on the road to progress, but after that, science will reach much greater heights.

Notice that the light and its surroundings are full of gaps, unexplained things and mistakes! This is because physics lacks a mediating substance, the aether, that connects matter. This essay clearly shows that even these simple experiments cannot be explained without the aether. Einstein said in a BBC lecture (1923) that "without aether, nature does not work.” Unfortunately, I have not managed to move forward.

15 March 2022  

Tom Tushey 

Mechanical engineer

 Hobby physicist 

Scientific Writer



Keywords: optics, experimental physicists, Zeeman, Fizeau,