Concerning the passage of light through a glass medium and it's apparent re-acceleration, is the absorption explanation supported by evidence? When someone questions how light can re-accelerate after slowing down in a glass medium, the common answer is that it never really slows down, it is absorbed by the atoms and then released.  Have there been any confirmations that this is the reason why light appears to slow down, or is this speculation, the best guess we have?  I'm thinking the apparent speed reduction could be estimated by knowing the density of the glass and calculating in the absorption/emission time?
What really causes light/photons to appear slower in media? 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:
What is the best choice for .NET inter-process communication? Should I use Named Pipes, or .NET Remoting to communicate with a running process on my machine? I have accounts in Stack Overflow, Programmers, Unix &amp; Linux and Area 51. I don't want to continue my Area 51 account, so I planned to delete my Area 51 account. I have performed the following steps to delete my account, but I couldn't!  Case 1     If your account has votes or posts do the following steps:         Edit the "About Me" section of your profile to say “please delete me”.   Contact the SE support to request deletion.      I edited my "About Me" section to "please delete me". When I contacted SE Support to delete my account, I couldn't make a request. I am getting the following error:  This operation is incomplete. please do it in main site.   For deleting Area 51 account, when I do it main site, in link for deletion column I gave the Area 51 link. It says that:  it is not valid link!   Case 2     If the account has not interacted with the site yet (votes or posts), click on the delete button on your user page next to the edit link.   I am not eligible for this case!  Then how to delete my Area 51 account? Any help is appreciated! The sum is $$\sum_{n=1}^{\infty} \frac{n+2^n}{n+3^n}$$ Is this convergent or divergent? I tried to use the divergent test but the test fail because $a_n = (n+2^n)/(n+3^n) = 0 $ as $n$ goes to infinity. Could someone point me to the right direction?  Thanks How to prove if $n$ is prime and $n | a^2$ then $n | a$? My professor assigned this for homework but I don't understand how to connect the dots. He suggested using the fact that $\gcd (x,y) \cdot \operatorname{lcm} (x,y) = xy$ but I'm not sure how that's relevant. How can I make schematic of this board? A few months ago I set full disk encryption during installation of Ubuntu 17.10. Now, I've decided to upgrade. The upgrade ran to the end without any problems. However, after reboot I am not able to log into my encrypted disk.  Where can be the problem? I am 100% sure I press the "right keys" on the keyboard, but technically I don't know what I am writing because of "*" characters and maybe after upgrade my keyboard layout changed. I use some characters which might be somewhere else on the keyboard. What language is default after upgrade?   By the way, I've already tried Caps-lock, but still no luck.  Help will be really appreciated. I am not a fan of installing my system and all backups over and over again. Inheritance in Java - creating an object of the subclass invokes also the constructor of the superclass. Why exactly? I have a question about inheritance in Java.  I have two classes A and B , and class B, inherits from A:  public class A {      public A() {          System.out.println("Hi!");      } }   public class B extends A {      public B() {          System.out.println("Bye!");      }       public static void main(String[] args) {          B b = new B();      } }   When I run program B, the output is:  Hi! Bye!      Question : why the constructor of class A is invoked, when I create and object of class B ?    I know that B inherits everything from A - all instance or class variables, and all methods, and in this sense an object of B has all characteristics of A plus some other characteristics defined in B. However, I didn't know and didn't imagine that when I create an object of type B, the constructor of A is also invoked. So, writing this:  B b = new B();   creates Two objects - one of type B, and one of type A.  This is getting interesting,   can somebody explain why exactly this happens? Evaluate $ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$ Evaluate $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$$  All i could do was to see that $$\frac{1}{3}=\frac{1}{2.1+1},\frac{1}{5}=\frac{1}{2.2+1},\frac{1}{7}=\frac{1}{2.3+1},\dots$$  SO, we should be able to write   $$ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots=1+\sum_{n=1}^{\infty}\frac{1}{2n+1}.\frac{1}{4^n}$$  This is what i could simplify the given question to...   But, this is doing me no good.. I could not go any further..  I would be thankful if some one can help me to clear this.  I would request users who are trying to help me to just give necessary hints but not post it as answer.  Thank You. Whenever I try to get somebody to follow me in Skyrim they something in the lives with "You already have a follower.". The problem is, I don't.   I have not, to my recollection, had a follower at any given point in the game.  The only thing I can think of is that I have (spoiler)      finished Anriel's Endeavors and gotten him as a summon creature.    Or do I have a hidden follower that I can't remember. A dog or a horse perhaps? Note that I do not have a dog or horse following me now. I talked to dog once, and had a horse that died.  Is this a common/known issue? Is there a work around?  Any tips? A 'for' loop to iterate over an enum in Java Does a non-EU Spouse of a UK national need a visa to visit the Schengen area? I am a British national resident in the UK. My wife is Jordanian, resident in the UK with me. She has a UK biometric residency permit. We were married in the UK and the marriage is registered in the UK.   Does my wife need visas to travel with me on holiday in France and Spain? I understand from EU Directives that she does not. Would we be able to leave the UK by ferry to France if my wife does not have a French visa but can prove that she is married to me and resident in the UK? If visas are necessary but the French or Spanish consulates were NOT to grant the visas, would this be in contravention of EU Directives/Law? If the answer to question 3 is "Yes, it would be unlawful", what action can one take to get the visas? Modular arithmetic: division, fractions, solving linear congruences I want to ask a question about modular arithmetic. I know, that modular multiplicative inverse exists only if modulo and integer are relatively prime. I want to know, are there any ways of division in modular arithmetic, if modulo and integer aren't relatively prime? I tried to find info about that, but failed. can I use same functions with the different type of argument inputs I've been told that when "the" is proceeded by a vowel sound, like "apple" or "hour", it's pronounced as "thee" and not as "thu".  But after listening to a couple of songs, I noticed that sometimes this "rule" is not followed. Take for example the two Katy Perry's songs, "Roar" and "The one that got away". In the first she sings "I got thee eye of thu tiger", but in the second she sings "Thu one that got away".  I don't know if it was sang this way to better suit the song melody (I understand nothing about those techniques), but I got confused. What's the correct pronunciation?  Thanks in advance. Make mouse left-handed and touchpad right-handed I see that I can configure mouse and touchpad all in one panel (Ubuntu 13.10, defaults, Gnome). Which is to some extend. Namely, I want to have the touchpad differently configured then the mouse and ...  When I have an (USB) mouse attached I use it normally left-handed. Therefore I switch the buttons to left-handed. But when I use the touchpad I feel little bit lost with that kind of configuration. Therefore I wanna have it right-handed.  Is there a way to achieve the following: when I plugin a mouse (respectively when it is detected) automatically switch to left-handed and when I unplug it, switch automatically to right-handed? Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$ Show that there exists a unique $v_0 \in H^1(0,1)$ such that $u(0)=\int_0^1(u'v_0'+uv_0), \forall u \in H^1(0,1)$. Further Show that $v_0$ is the solution of some differential equation with appropriate boundary conditions. Compute $v_0$ explicitly.   Let $f: H^1(0,1) \to \mathbb{R}$ be defined by $f(u)=u(0)$. Then I showed that $f$ is linear and continuous. Hence there exists $v_0 \in H^1(0,1)$ such that $u(0)=\int_{0}^1u'v_0'+\int_{0}^1uv_0$  The differential equation is given by $f=-u''+u$ with the conditions $u'(0)=u'(1)=0$.   How do I compute $v_0$ explicitly?? Include custom taxonomy term in search I have two custom taxonomies applied to two custom post types. the terms list on the sidebar just fine and will list all posts associated with it. However, if you search one of the terms in specific, it doesn't bring up a post with that term.  Example:  Search for term "PQRI"  I get nothing. Any ideas? I've tried using various search plugins but they either break my custom search parameters or just don't work. Determining confidence interval with one observation (for Poisson distribution) $G$ solvable $\implies$ composition factors of $G$ are of prime order. I'm trying to prove the equivalency of the following definitions for a finite group, $G$:  (i) $G$ is solvable, i.e. there exists a chain of subgroups $1 = G_0  \trianglelefteq G_1 \trianglelefteq \cdots \trianglelefteq G_s = G $ such that $G_{i+1}/ \ G_i$ is abelian for all $0 \leq i \leq s-1$  (ii) $G$ has a chain of subgroups $1 = H_0  \trianglelefteq H_1 \trianglelefteq \cdots \trianglelefteq H_s = G $ such that $H_{i+1} /\  H_i$ is cyclic for all $0 \leq i \leq s-1$.  (iii) All composition factors of $G$ are of prime order.  (iv) G has a chain of subgroups $1 = N_0  \trianglelefteq N_1 \trianglelefteq \cdots \trianglelefteq N_t = G $ such that each $N_i$ is a normal subgroup of $G$, and $N_{i+1}/ \ N_i$ is abelian for all $0 \leq i \leq t-1$.  It was simple to show that (iii) $\implies$ (ii) and (ii) $\implies$ (i). Now, I'm trying to prove that (i) $\implies$ (iii), and I'm getting stuck.   I know that If $G$ is an abelian simple group, then $|G|$ is prime, so all I need to show is that each $G_{i+1}/ \ G_i$ in the definition of solvable is simple.  If I knew that $1 = G_0  \trianglelefteq G_1 \trianglelefteq \cdots \trianglelefteq G_s = G $ were a composition series, then each $G_{i+1}/ \ G_i$ would be simple by definition. But the definition of solvable doesn't assume a composition series. I know every group has a unique composition series, but I'm not sure how to connect that to the subgroups in the definition of solvable.   More generally, I guess I just don't understand how being abelian connects to being of simple or of prime order.  Any pushes in the right direction would be appreciated! What is a mixin, and why are they useful?