Do we see in 3 dimensions?

Hi,
its been quite long time since I wrote about dimensions. Just a quick recap since people do not click on links much: 0th dimension is point, 1st dimensions is line, 2nd dimension is plane and 3rd dimension is space. We are talking about spatial dimensions, another thing is atime dimension, but that is not important here.


So I got into this argument if humans see in 3 dimensions or not, I got no clear conclusion though so I am just going to discuss it here. We live in 3 spatial dimensions, proof, cubes exist. How do we see though? We can see cubes but I would argue that we see in 3rd dimension.

  1. Retina does not capture depth, it is 2 dimensional detector so we simply can not have a 3 dimensional vision.
  2. We have two eyes though, lot of people seem to like to point this out. With second eye you have what is called a stereoscopic vision.. the second eye has little bit different point of view and when brain combines it stuff gets depth. This does not mean that we see in 3D though. Still it is just two 2 dimensional pictures put together. Brain interprets this picture as 3 dimensional and based on experience judges distance. Also colors and shades can help us with that.

    File:3D stereoscopic projection icositetrachoron.PNG

    This is stereoscopic picture, disalign your eyes and match the pictures so you see 3 of them.

  3. You can draw anything you see on piece of paper and it will be exact representation of what you see, all angles same and so on. This I think would be impossible if you actually wanted to transfer 3D image to 2D plane because by definition 3D space is made up of infinite 2D planes put on top of each other. Same as you can not take infinite picture and store it in 1D line.
  4. If we could see in 3D we would see all angles as they actually are. If you look into corner you do not see 90° angles though because you remember the way that walls work you know that they are there.

Thats about the arguments I have, hope you enjoyed reading,

Dragallur

Why do stars twinkle (and planets not)?

Hi,
I felt so embarassed that I finally had to find it out and now I am writing this short post about it. For few years, roughly, I am studying astronomy yet, I never knew why stars twinkle and planets not. I confess.


Stars twinkle because the light that reaches us goes through atmosphere and atmosphere is not very homogenous – smooth. Air refracts light and there is different temperature once in a while, humidity and so on, I think that lot of factors play the role. This causes the light of star to scatter a bit and creates the twinkling effect.

Planets do not do it. This is great because you can identify them extremely fast on the sky and you do not mistake them for some other bright star. Why? Their light still goes through atmosphere. Because they are not “point sources”. Stars are so far away that even with best telescopes we see them only as points. Planets with simple telescope on backyard already have shape. Some of their light scatters one direction, some the other and it basically cancels out creating nice image. This is also why it is better to go star-gazing in the winter, colder air does not create so much “noise” on the picture.

Dragallur

Your phone is NOT killing you

Hi,
today I want to write about ionizing and non-ionizing radiation and also mobile phones as serial killers.


When somebody says radiation they mean electromagnetic radiation. Light is of course an electromagnetic radiation but only small part that we can see.

Visible light makes only very small part of whole spectrum.

The energy of light is connected with its frequence, as it rises (to left) energy increases as well. Gamma rays are the most energetic part of spectrum, they appear in radioactive decay and the are also created in Sun. Radiowaves on the other hand have enormous wavelength and very small energies, this is very good because it means that they are easy to create and also not harmful to human.

When we talk about radiation we can say that it is either ionizing or non-ionizing. If it is ionizing it means that it can create ions. Ions are either positively or negatively charged atoms, ions are created when they get or lose an electron which happens when photon hits the electron, but not always. If the energy of the photon is high enough then it will happen (ionizing) but if it is not the nothing will happen (non-ionizing).


How does this corresponds to your phone?

Well there have been some studies that showed that frequent phone users had higher chance of getting brain tumor. This would be caused by the photons that are transmitted from your phone. They should apparently hit DNA and other stuff in your cells and by ionizing these atoms, make change and possibly develop cancer.[0]

The radiation that is used in your phone is with the wavelength of tens of centimeters which means something like low radiowaves. Photons in this part of spectrum would not be able to knock electrons from atoms at all [1].

While for example study from Sweden showed that brain tumors and phone usage correlates, the study was not so well made. The problem is that you need gigantic sample since brain tumors are very rare (3/100,000 people). In short, the best thing you can do is to look on the number of brain tumors before “everyone” started to use cell phone and compare it to the number brain tumors right now…

SPOILER AHEAD

There is no correlation whatsoever!

Dragallur

If you want more detail about the studies and so on, check out these two videos:

[0] I was just thinking that if radiowaves cause cancer than we should probably be much more conserned about ultra violet that is roughly million times stronger!

[1] Einstein got Nobel prize for finding the photoelectric effect which is basicly the knocking of electrons by photons. He found out that under certain frequency the atoms will not be ionized because the energy is not high enough (this critical point is different of course for different elements).

 

 

Optics: 7) So is it wave?

Hi,
in last post I was talking about the experiment that proved that light is wave, it is creating interference in the double slit experiment instead of two lines which one would assume if it was behaving as a particle. (You can imagine bullets instead of particles).

double-slit-bullets

If light was behaving as particle


So I found out that the particle part of light is bit more complicated so I wont try to explain it so much in the PRO sense but rather in few words, if you are more interested check out this page: 1)

With this theory that light is just a wave there were finally find some problems.

If you would very accurately measure light on some spot and this light would be dimmer and dimmer, you should get dimmer and dimmer picture. But at one point there were just dots!

ccd-spot

As the light is getting dimmer, with very good camera you can see that some pixels get much more energy than other.

As you might understand this was quite confusing. Wave should not make pattern like this.

Soon it was found out that when you measure brightness you can find bumps that should not be there if light would be wave, rather it should be quite uniform.

Finally what was concluded from this is that light behaves both as wave and particle, the attribute is called particle-wave duality.


What was also found at this time (something like beginning of 20th century) is that light comes in quantas. This has very interesting effect. If you would walk away from candle and would be able to distinquish individual photons at one point the candle would not shine less and less because at one point there will be only one quantum coming to you and quantum is not divisible so it would start to disappear more and more often but it would always shine. More detail here:

It was also found that not only photon but also other subatomical particles behave like waves and particles. In 20th century it was tested with electrons and sure! They also made this interference pattern on detector.

Dragallur

PS: This is my 200th post!

 

 

 

 

 

Optics: 6) Experiment that changed our thinking

Hi,
today I will again write about optics but I have to return at the very beginning of 19th century when Thomas Young proved that light is behaving like a wave.


So there was this problem.

Newton thought that light has to be lot of particles, he called them corpuscles.

At the same time Huygens thought that light is behaving like a wave.


Then came this smart guy called Young. He conducted easy experiment to prove this.

The experiment is based on phenomena called interference of light. Imagine two people calling. When they both call at the same time. The called person is more likely to hear the call because they amplify the sound together. Now imagine that they want the person to hear some word that they are repeating again and again, such a word could be: RETURN!

When they call both at the same time it will make mega RETURN! And you can be sure that the person will hear it. But if one of them is slower by just a fraction of the time that it takes to say the word, whole message is destroyed:

1st person:   |return!|
–>  RETURN!
2nd person: |return!|
1st person:   |return!|
–> retuRneturn
2nd person:         |return!|
From the second example you can clearly see that if it is just a little windy the message may end up some thing like: “ertueruterut” and that is something you do not want. So light behaves in the same way. If both lasers are calling “red” at the same time you will get mega red (amplyfied red, with higher amplitude). If not well, you know what happens!

But analogies can take as only so far. There is one more problem. In my example if one person would call: “return” and the other “go away” the message should be destroyed. But with light, nothing happens, the words (colors) do not interact at all (in this way) because to interact the frequency has to be the same, this is called coherence of light.


So how did he use the interference of light to prove that light behaves like a wave? In his experiment imagine having a dark room with one small hole that leads to another two holes like this:

As the light passes through both slits it creates interesting pattern that is unique for waves.

If light would be particle you would see two lines on the right. But instead what happened was that at some places the amplitude was increased, as both sources (both slits) were calling (shining) at the same time or they were just moved by one word (one top of wave).[1] So some of the light is in consctructive interference (peaks on the black line) and some parts of the wave is in destructive (bottoms of the black line). This creates lighter parts and darker parts:

The double-slit experiment

And finally animation:

The light passing through both slits, green part is destructive, blue, red and yellow constructive.

Dragallur

If you are not still sure about this, watch the video below:

[1]By this I mean that one person starts calling: “return return return” and the second joins for the second return so they are moved by one period.

 

 

 

Why do we use CMYK instead of RGB? (Very colorful post)

Hi,
maybe you too wondered why there is written CMYK on printers. If you have printer or you found out what it means you too know that it is abbreviation for: Cyan, Magenta, Yellow (and K which I will tell later).

What CMY stands for?

 

 


Those are the colors that you have to fill inside the machine to print you stuff. Sure this is ok, but why do not we use RGB (red, green, blue)? It seems to be used everywhere so why not in printers?

I thought this because I was thinking that from RGB you can get any color, and sure you can, but only in additive process. Such a process happens for example with light, white light is made up of many different parts with different wavelengths that ADD up. So what does mean that something is red(?), well it reflects only red light absorbing the rest. If you put there blue the material will be even more darker because it will reflect only the combination of blue and red. If you combine everything it would not reflect at all, the object would be black.

This is an example of substractive process with colors. You can see that RGB is darker since you will get it by substracting CMY.

So what you want to do is to start with lighter colors, those are cyan, magenta and yellow. They too are able to add up to all other colors + lighter than RGB in this subtractive form. Even then colors are not perfect in printers so you can not add up to some, bright red, blue  and green wont be displayed very well.

 

 

 

 

 

 

What the “K” stands for? It stands for “Key” which is the color black (it is the KEY thing). While CMY can add up to black, it would not be very pure since the colors can not be clean, it was decided that there will be black added because in most texts black is used. The letter “K” was used because “B” was already used in the RGB model.

Dragallur

PS: check out these two links about colors shared by Jim Ruebush, they are truly amazing:
1) 2)

 

How does optical fiber work?

Hi,
so again, as I was studying some optics I found something that interested me. This time it was optical fiber which is the cable that may be running under your way to work bringing you some interner connection.


Optical fibers are cables that are carrying signal. They are made of two pieces of glass with different indexes of refraction. When electromagnetic radiation (light) travels through this tunnel that is made by this cable it bounces off the sides if it is in big enough angle.

There is value called critical angle in which light will always bounce on the edge of two mediums. It depends on refractive index.

This kind of communication is very useful one because glass is very cheap compared to some metals and the communication can not be destroyed by some magnetization. Also

The optical fibre has to be protected in some material, the core itself may be in micrometers.

Optical fibres are usually packed in nice groups.

 

 

 

 

 

those tubes made up of glass are quite flexible.


 

By transmitting signal on one side usind some diode you can few kilometers away decode this signal based for example on the number of pauses and number of incoming light waves. Such a communication may reach amazing speeds of tens of gigabytes per second.

There are two main types of optical fibers. First one are multi-mode fibers.Those are the ones for a shorter distance, roughly 600-1,000 meters. There is lot of light running there and it is used to deliver signal in buildings. If you would use it for longer distance the light would stop traveling predictably.

The second type is single-mode fiber. This is much thinner and works on the distance of tens of kilometers. It is used between countries and cities.

Dragallur

 

 

 

Cycling faster than light

Hi,
so while I was learning some optics, I bumped into this page that talked about refractive index which I was just studying. I wondered what is the highest refractive index ever found and there it was, not in number though I think we can calculate it.


Refractive index

Since you probably have not read my post about refractive index or you have not heard about it, it is dimensionless value that shows how much is light (electromagnetic radiation) slow in the medium where it travels and also how much it will change its direction when traveling through one medium into the other. You can calculate the index like this:

n=c/v

Where n is the refractive index, c is speed of light in vacuum and v is the velocity in the medium you are talking about. From this, it is easy to see that vacuum and only vacuum has the refractive index exactly 1 because there is nothing that blocks its way and you just divide speed of light in vacuum by speed of light in vacuum.


So as the index of refraction increases the only thing that can change is velocity in the medium and it is decreasing.

I found that scientists were able to create stuff in which the light was traveling in “only” 17 meters per second! This is 61.2 kilometers per hour. From steep hill or if you are really good cyclist you can be faster than that, though I think it is bit more easier and safer to do it in car.

So what is the refractive index of this miraclous stuff? Roughly 17,647,059. While normally n lies somewhere between 1 to 3.

What is this thing made of? 

… gas of sodium atoms – a high-tech version of the insides of the bulbs of street lamps – cooled to within a fraction of a degree above absolute zero … the effect of cooling reduces thermal effects, and this in itself contributes to the retardation of light.

There is also special state of matter created that packs those atoms closer together.

Dragallur

 

Why are radio telescopes so large?

Hi,
take a Hubble telescope, it has primary mirror 2.4 meters tall. Now take this:

Arecibo Observatory Aerial View.jpg

The giant Arecibo radio telescope

I mean the thing above which is Arecibo radio telescope has diameter of 305 meters. Both things are for the same thing, to observe the Universe.


So the answer lies in the name. Arecibo is a RADIO telescope which means that it works on quite different wavelengths, actually magnitudes bigger wavelengths since the wavelength of for example visible light for Hubble is 550 nanometers which is quite small while radio waves can have wavelength of hundreds of meters.

This is essentially the key. If you want to see clear image in light (that we can see) you need just a small telescope. Both work the same way though from what I understand you need larger area to collect all of those waves and reflect them on the focus which is above. The equation shows it clear:

θ=1.22*λ/D

Where θ shows how close two points can be to each other without you being able to distinquish them. λ is the wavelength of the light and D is the diameter of your telescope. So you will see best when wavelength is small and diameter is huge since this will lower the angle that you are not able to distinquish. Of course that there is huge difference when you insert meters instead of nanometers so you must compensate it with the diameter of the telescope.[1]

If you want to have a clear image in radio waves, well you have to build Arecibo.. really? Isn’t there another option?

Yes there is! You can build a lot of small radio telescope that would alone be very weak but if you take lot of them you can have a Diameter of kilometers. Such a device is called interferometer which means that is “operates by myltiplying the data from each pair of telescopes together to form interference patterns”.

There is more of them and this one is ALMA observatory.

So those are huge fields or rows of smaller (even 60 meter) discs that collect data. They have to be extremely accurate what is time concerned (atomic clocks).

Dragallur

[1]1.22 is just an empirical value.

Can you see a coin from 400 kilometers?

Hi,
no, probably not with naked eye, I think, though if it would be some special coin, maybe? The point is that you can use some cool things to see such a coin, for example Hubble Space Telescope!


Ok, I found some page with physics problems and one of the first was to calculate what is the smallest angle that Hubble Telescope can distinquish. I calculated that it is roughly:

0.0127”

This means 0.0127 arcsecond!!!

How far away football has to be to have the angular diameter of one arcsecond

What about a human eye how good is it? Well eye can distinquish only things that are 1′ away from each other [1], which means one arcminutes, one degree has 60 of those so it is pretty good but not so much as Hubble. But anyway, back to the title, how small is a coin?

I measured the second largest Czech crown to have 2.55 centimeters.

Now how far away do you need to be to not be able to see it with naked eye? We will use this formula to get the diameter:

θ=D/r

Where the diameter (D) is 0.0255 meters. The distance (r) is what we are trying to find and the angle eye can distinquish is θ (in radians). [2]

r=D/θ

If all the calculations went right it should be:

r=87.6625 meters

But beware this is not counting air, humidness and so on so you will most certainly not be able to see coin on this distance.

What about the Hubble telescope? We can use the same equation but for θ we will insert much smaller value!

And yes, you can see the coin from 414,153.744827 meters! Which means that you can see one freaking coin from London 50 kilometers behind Paris! One coin![3]

This is so cool.

Dragallur

[1]You can try this by drawing two dots on paper and then moving away from it, at one point when you are far enough you should be able to see only one.

[2]This equation is simplified but it should work for small angles.

[3]Again, this works only in space because there is nothing that would block your sight.