While researching the cause of refraction, I found that refraction occurs due to the change of speed of light when it goes from one medium to another (according to Huygens principle).  But I cannot get why actually does its speed change when the medium changes?
I know that if we solve the Maxwell equation, we will end up with the phase velocity of light being related to the permeability and the permittivity of the material. But this is not what I'm interested in - I want to go deeper than that. We know that the real speed of light is actually not changing, the decrease in speed is just apparent. Material is mostly empty, the light will still travel with $c$ in the spacing. The rare atoms will disturb the light in some way. So I am interested in how the atoms affect the light. Photon absorption-emission theory Some textbooks that I read explain it in a way kind of like this: In a material the photons are absorbed by atom and then re-emitted a short time later, then they travel a short distance to the next atom and get absorbed&amp;emitted again and so on. How quickly the atoms in a material can absorb and re-emit the photon and how dense the atoms decides the apparent speed of light in that material. So the light appears slower because it has a smaller “drift speed”. Interference theory But recently I realize an alternative explanation: Atoms respond to the light by radiating electromagnetic wave. This “new light” interferes with the “old light” in some way that results in delayed light (advanced in phase), this can easily be shown by using simple phasor diagram. Consequently effectively the light covers a smaller phase each second, which gives the impression of a lower phase velocity. However the group velocity is changing in a complicated way. I think that the first explanation does not explain the change in phase velocity of light. if we consider light travelling into a slab of negative refractive index non-dispersive material, let’s say the light is directed perpendicular to the slab. The phase velocity’s direction will be flipped, but group velocity’s direction in the material will not change. Only the second explanation can explain the flipped phase velocity direction. I guess that the velocity that we get in the first explanation is actually belongs to the group velocity. It makes sense to me that the front most of the photon stream determines the first information that the light delivers. So the question is What really cause the phase velocity of light to be decreased?  &quot;drift velocity&quot; of photons (they aren't the same photons, they are re-emitted all the time) phase difference between absorbed and emitted light something else  And also, I still don't really understand detailed explanation of the absorption-emission process for small light's wavelength (for large lambda compare to the atoms spacing, the photons will be absorbed by the phonons). The dispersion relation that we know is continuous and also some material is non-dispersive, therefore the absorption process must occur in all frequency for a certain range. So definitely it doesn't involve the atomic transition, otherwise it will be quantized. My guess is that the relevant absorption process gets smooth out by the dipole moment. What makes the spectrum continuous? EDIT: link for dispersion relation:
Set spawn point for a specific player I made a server and me and one of my friends want to do a prank on another friend, because he stole all my enchanted diamond armor.  The Prank  I want to set a player's spawn point in a pit of lava, how would I do this without affecting anyone else's spawn point? Why is SQL Server losing a millisecond? I have a table structured like this:  CREATE TABLE [TESTTABLE] (     [ID] [int] IDENTITY(1,1) NOT NULL,     [DateField] [datetime] NULL,     [StringField] [varchar](50),     [IntField] [int] NULL,     [BitField] [bit] NULL )   I execute the following code:  BEGIN     INSERT INTO TESTTABLE (IntField, BitField, StringField, DateField)     VALUES ('1', 1, 'hello', {ts '2009-04-03 15:41:27.378'});       SELECT SCOPE_IDENTITY()   END   And then   select * from testtable with (NOLOCK)   and my result shows:  2009-04-03 15:41:27.*377*   for the DateField column.  Any ideas why I seem to be losing a millisecond?? I have joined corresponding Local Enterprise Partnerships table data into a polygon shapefile containing UK Local Authorities.      How do I Dissolve or Merge the the Local Authorities polygons by LEP_NAME as shown in the screenshot?   Ideally, I would like to retain the Local Authority attributes with the resultant merged polygons. I have zero scripting knowledge so am looking for a tool based solution. Any help or pointers much appreciated.    Additional Note: When attempting to use the dissolve tool the LEP_NAME field is not available as shown above. The LEP attribute data was created in Excel, saved as CSV format and joined to the Local Authority polygon shapefile. There are duplicate IDENTIFI0 fields as shown in the other screenshot - could this be the root of the issue? Can ASP.NET MVC generate elements with lower case name and id attributes I'm trying to amass a list of physics books with open-source licenses, like Creative Commons, GPL, etc. The books can be about a particular field in physics or about physics  in general.  What are some freely available great physics books on the Internet? edit: I'm aware that there are tons of freely available lecture notes online. Still, it'd be nice to be able to know the best available free resources around.  As a starter:         Table of contents sorted by field (in alphabetical order): Is the converse of Cayley-Hamilton Theorem true? The question is motivated from the following problem:     Let $I\neq A\neq -I$, where $I$ is the identity matrix and $A$ is a real $2\times 2$ matrix. If $A=A^{-1}$, then the trace of $A$ is   $$ (A) 2 \quad(B)1 \quad(C)0 \quad (D)-1 \quad (E)-2$$   Since $A=A^{-1}$, $A^2=I$. If the converse of  is true, then $\lambda^2=1$ and thus $\lambda=\pm1$. And then $\rm{trace}(A)=1+(-1)=0$.   Here are my questions:   Is  $C$ the answer to the quoted problem?  Is the converse of Cayley-Hamilton Theorem, i.e.,"for the square real matrix $A$, if $p(A)=0$, then $p(\lambda)$ is the characteristic polynomial of the matrix $A$" true? If it is not, then what's the right method to solve the problem above? For example, when I type ping 8.8.8.8 &amp;, why can we see ping process working? And when I type find / -name '*test*' &amp; , it's also seen on monitor.  Why is that? Is it not really in background? Yesterday I read Modern English:A Practical Reference Guide written by Marcella Frank, and she gives a paradigm about tenses on page 50. The page shows tenses in active voice and passive voice; she said these four tenses are exceedingly rare:   shall/will be being offered has/have been being offered had been being offered shall/will have been being offered   Why are these tense so rare? Are they normally replaced by other tenses? I have been getting this question lately from students and although I have a lot of information to offer, I have not found a source that I can point people to where they can read an update answer (I have found a lot of misinformation and obsolete information). So, some of the questions I have for package formats like snap, appimage, flatpak and others in this evolution of universal packaging systems are:   Who created the package format? What features does it offer? What features are unique to it? (That the others do not yet have) Who supports it? What Distributions use it? What focus does the package have? (For Desktop, Clouds, Mobile, etc..) Which are more actively developed? Can't pair apple wireless keyboard Keyboard: Apple Wireless Keyboard (model number MC184LL/B)  System: Macbook Pro Early 2011 running OS X 10.8  The keyboard gets detected and when I try to pair it, the system asks to enter some numbers through the keyboard.   However when I press the key (on the wireless keyboard) nothing happens, the only key that seems to work (i.e. to move to the next key in the code) is 0. I can also press enter to confirm but it always fails (since the only code I can enter is 0000...0).   I've also tried pairing from the bluetooth preference and changing the passcode option. However this won't work either.   Any ideas? The keyboard was paired with another MacBook Pro (I don't have access to it anymore). Is there any method to 'reset' the keyboard to factory settings? I read this book series in middle school. I believe that it would be classified as young adult fiction/fantasy. A girl has magical powers, and with her growing powers comes runes/tattoos in her arms. This is shown on every book cover. I know that one cover is blue. This one shows the girl in a black tank top and black pants. One is a yellow cover, with her in a dress (I think).  The girl has a friend/mentor, who she develops feelings for. The girl is the key to stopping a war between multiple factions/people. Each side is trying to use her to their advantage. I think the series was written in the early 2000s. Are those stars moving past the window when the ship is at warp? When the enterprise (ENT) is moving at warp we see numerous stars flying past in the windows:    However, according to , at warp 5 (the maximum speed of the 1st enterprise) it would take 7.4 days to get from the Sun to Alpha Centari, our nearest star(s) approximately 4 light years away. So to have stars whizzing past every few seconds would imply that the stars are very close together.  Is this an inaccurate depiction of star movement at warp, or is there some explanation like the warp bubble creates a lensing effect?  Now I realise the classic answer is "suspend your disbelief, it's a tv show", but the animators have at least thought about the star movement as they have added in a bit of red shift and blue shift which you can see in the image. kidle_inject causing very high load Whenever kidle_inject starts running on my system the load shoots up. In general it only gets to a load of around this 5.23, 3.65, 2.54 but a lot of the time it jumps up past the 15 mark on each of them. At that point the system grinds to a halt and I have to power it off.  This only happens when the kidle_inject process starts. How can I disable this process so my machine can work and I can get some work done.  Example top:  top - 12:43:48 up  3:02,  3 users,  load average: 6.57, 5.53, 3.33 Tasks: 256 total,   3 running, 253 sleeping,   0 stopped,   0 zombie %Cpu(s):  5.9 us, 16.6 sy,  0.0 ni, 74.7 id,  0.5 wa,  0.0 hi,  2.3 si,  0.0 st KiB Mem:   8080252 total,  7937856 used,   142396 free,   258904 buffers KiB Swap:        0 total,        0 used,        0 free.  4061336 cached Mem    PID USER      PR  NI    VIRT    RES    SHR S  %CPU %MEM     TIME+ COMMAND 13509 root     -51   0       0      0      0 S  54.7  0.0   3:29.47 kidle_inject/1 13511 root     -51   0       0      0      0 S  54.1  0.0   3:30.92 kidle_inject/3 13510 root     -51   0       0      0      0 S  48.8  0.0   3:11.60 kidle_inject/2 13508 root     -51   0       0      0      0 S  47.6  0.0   3:08.47 kidle_inject/0 The Windows Domain I manage has hundreds of computer names which I don't recognise and I'd like to remove old ones which aren't in use before trying to track down the misnamed ones.  Is there someway to see when the last time a machine logged onto the network? Either via dhcpd or a user login event or something else. Can we continue to show the "Take a tour" banner after a user has created an account? Questions about insects eating flour and living in the cracks of a wooden cutting boards I have a large wooden cutting board which is used in my kitchen mainly for preparing egg pasta. The wood type is Populus (poplar or aspen or cottonwood).  The main ingredients used with the cutting board are: flour (mainly soft wheat flour), hens' eggs, white sugar, butter, and baking powder.  After the food preparation, the cutting board is cleaned by scraping away the ingredients remains.  The board has some cracks and some small unknown insects are living inside the cracks.   The board has also a lot of holes due to woodboring beetles but I think the woodworms operated long time ago and they no longer live in the cutting board.  The unknown insect has an approximate length of 1 mm (along the direction of their movements) and a width of 0.3 mm. The unknown insects do not have wings, they just walk. I am not able to see how many pairs of legs they have.  The color of the insect is pale brown.  The cutting board was free from these unknown insects some months ago but then they appeared.  My questions:   What insects are they? Are these insects poisonous to humans? How can I get rid of them?   Update  The unknown insects could be Acarus siro, I will try to get a picture of the insects.  Update 2  Here is a picture. The bottom part of the image is a one Euro coin, the top part of the image is a caliper (each bright area is one mm tick).   Some more pictures: Is it possible to search every field of every table for a particular value in Oracle?  There are hundreds of tables with thousands of rows in some tables so I know this could take a very long time to query. But the only thing I know is that a value for the field I would like to query against is 1/22/2008P09RR8. &lt;  I've tried using this statement below to find an appropriate column based on what I think it should be named but it returned no results.  SELECT * from dba_objects  WHERE object_name like '%DTN%'   There is absolutely no documentation on this database and I have no idea where this field is being pulled from.  Any thoughts? Consider a complete metric space $(X,d)$ and $T\colon X\to X$. Suppose there exists $n\in\mathbb{N}$ such that the n-th power of $T$ is $q$-contractive. Show that then $T$ has exactly one fixed point $\overline{x}\in X$.      The n-th power is defined inductively: $$ T^{n+1}(x):=T(T^{n}(x)), n\in\mathbb{N}. $$ And for a function $T\colon X\to X$, $q$-contractive means  $$ \exists 0\leq q&lt;1~\forall~x,y\in X: d(T(x),T(y))\leq q d(x,y). $$    Now to the proof.  I think I have to show, that $T$ is q-contractive, because then it follows with Banach, that $T$ does have exactly one fixed point. So I have to show, that there exists a $0\leq q&lt;1$ so that for all $x,y\in X$ it is $$ d(T(x),T(y))\leq q\cdot d(x,y). $$ And most likely I have to use the q-contractivity of $T^n$, i.e. that there exists a $0\leq q &lt;1$ so that for all $x,y\in X$ it is $$ d(T^n(x),T^n(y))\leq q\cdot d(x,y). $$  Can you help me? Why was Edo Tensei Madara young, when he had died at an old age? From Naruto manga and anime, I know that Uchiha Madara died as an old person after he helped Uchiha Obito.   But it was bit weird for me, when Kabuto summoned Uchiha Madara-sama with Edo Tensei, Madara was a younger person.  Again, when Chiyo was summoned, she was older as when she died.  How can it be possible? Retain precision with double in Java