does the refractive index of a medium depends on wavelength of light passing through it ? If yes then why ?
Why do different wavelength get impeded more or less when in different materials? Moving with the same speed, but a longer physical distance would imply that the fields oscillate less times in the material, but I don't know why a difference in the number of oscillations would impede the wave- I don't even know why things slow down in general. Why some electromagnetic wave would slow down just because it's entering other electromagnetic fields... It would seem to me that the only factor would be time taken to physically move some electron or something in the direction of the fields... But that seems to simple of an explanation to me.
mysqli bind_param for array of strings I get this error message   NMI watchdog: BUG: soft lockup - CPU#2 stuck for 23s! [plymouthd:305]    on the startup of my system (even with live-cd).  My PC is a dell inspiron 7559 with intel graphic and nvidia.  UPDATE - this issue also happens when attempting to install ubuntu 18.10 using LiveUSB Finding package name of installed software Since I have not been able to open Dash Home in 12.04.4 see , I am hoping for a work-around. Is there another convenient way to open apps/programs without having to search through folders? Is this question clear enough? For example, I just installed Kile (publishing program) from the Software Center, but I can't find a link/tile/icon/shortcut to open it. Thanks, to whomever can help. Show only hidden files (dot files) in ls alias Why are there two tensions on my free body diagram? A man sits on a platform attached to a pulley and pulls himself up as shown (ignore the angle of the rope - it should be vertical). Apparently, the man/platform object has a force of 2T pulling it up. Why is it not just T?  Much appreciated! If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$ Intellij shortcut for quick call hierarchy Is there a shortcut key to bring up the call hierarchy of a method inline with the code, in the quick menu format, rather than bringing up the call hierarchy panel? Proving the two given vectors are orthogonal I am given the vectors $\mathbf{w}, \mathbf{v}, \mathbf{u}$ in $\mathbb{R}^n$ such that $\mathbf{u} \neq 0$ and $\mathbf{w} = \mathbf{v} - \frac{\mathbf{u}\,\bullet\,\mathbf{v}}{\|\mathbf{u}\|^2}\bullet\mathbf{u}$. I am asked to show that the vector $\mathbf{w}$ is orthogonal to $\mathbf{u}$.     So far, I have written out the definition of orthogonal: two vectors are orthogonal if and only if their dot product is zero.   So what we need to prove is $\mathbf{w}\bullet\mathbf{u} = 0$ where $\mathbf{w}\bullet\mathbf{u}$ is defined as $\mathbf{w}^T\bullet\mathbf{u}$.   However, I have been stuck on this problem for about an hour and haven't made any significant progress from here. How do we go about proving that the vectors are orthogonal? How do you deal with a player that's determined to play the game in a way that is detrimental to the advancement of the story? Why must I wait two days before accepting my own answer? I got this message today while trying to accept my answer on my own question.  Why must I wait this time, if I am sure that the answer I answered is the right one, just want to understand the point of view?  I faced that just today on Super user and didn't get this message before. Can we balance the whitespace above/below headings? In January, some additional whitespace  below h1, h2 and h3 headings,  more whitespace below the headers than above them.  Could we have the whitespace above the headings be more than the whitespace below them?  I find some posts a bit hard to read, like the current rendering on the left:   &nbsp; &nbsp; &nbsp; Solve $z^2+|z|=0$ Solve for $z$: $$z^2+|z|=0$$ I found this question on my textbook but I unable to derive an answer to it as a modulus of $z$ is present. I am unable to take an approach please guide me ..thanks I have a simple 2-column layout with a footer that clears both the right and left div in my markup.  My problem is that I can't get the footer to stay at the bottom of the page in all browsers.  It works if the content pushes the footer down, but that's not always the case. Help with proof of $|x+y| \geq |x|-|y|$ Let $E$ be a Banach space, $\mathcal B(E)$ the Banach space of linear bounded operators and $\mathcal I$ the set of all invertible linear bounded operators from $E$ to $E$. We know that $\mathcal I$ is an open set, and if $E$ is finite dimensional then $\mathcal I$ is dense in $\mathcal B(E)$. It's not true that $\mathcal I$ is dense if we can find $T\in\mathcal B(E)$ injective, non surjective with $T(E)$ closed in $E$, since such an operator cannot be approximated in the norm on $\mathcal B(E)$ by elements of $\mathcal I$ (in particular $E$ has to be infinite dimensional).  So the question is (maybe a little vague): is there a nice characterization of $\overline{\mathcal I}^{\mathcal B(E)}$ when $E$ is infinite dimensional? Is the case of Hilbert space simpler? facl ignoring the "x" permission but only on files When I use setfacl to manage on what permissions should the children files / directories have, for some reason the files have all the permissions except the execute ("x") one.  someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ getfacl . # file: . # owner: someuser # group: webs # flags: -s- user::rwx group::rwx other::rwx default:user::rwx default:group::rwx default:other::rwx  someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ touch file someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ mkdir dir someuser@someuser-MS-7816:/opt/lampp/htdocs/project$ ls -l total 4 drwxrwsrwx+ 2 someuser webs 4096 paź 31 13:35 dir -rw-rw-rw-  1 someuser webs    0 paź 31 13:35 file   I thought it has something to do with umask but changing it in various ways never gives the expected result unless I'm missing something.  How can this be fixed? I am taking an abstract algebra course and I am really interested about the topic.  So much so that I spend most of my time reading supplementary materials.  I consequently know a lot more theorems than the ones covered in class.    In a recent quiz, I used a theorem in one of my proofs that was not mentioned in the lecture since.  My professor gave me partial marks for my answer for the reason that we didn't cover this theorem in class even though the proof was completely valid!  I can't really see where he is coming from.  How would someone be able to use a theorem correctly if he doesn't know its proof?  I was quite baffled by his comment.   Do you agree with this?  EDIT: The professor just Emailed me and said that after thinking for a while, he decided to award me the full mark for the question. He also mentioned that he didn't want discourage me from studying the subject (since he saw most of my previous quiz grades were full marks) and I was passionate about it, but kindly requested that I include any proof for a theorem that I cite from now on in his exams. He also sent a broadcast message to the whole class indicating this. Find all solutions to $x^2\equiv 1\pmod {91},\ 91 = 7\cdot 13$ I split this into $x^2\equiv 1\pmod {7}$ and $x^2\equiv 1\pmod {13}$.  For $x^2\equiv 1\pmod {7}$, i did: $$ (\pm1 )^2\equiv 1\pmod{7}$$ $$(\pm2 )^2\equiv 4\pmod{7}$$ $$(\pm3 )^2\equiv 2\pmod{7}$$ Which shows that the solutions to $x^2\equiv 1\pmod {7}$ are $\pm1$.  For $x^2\equiv 1\pmod {13}$, i did: $$ (\pm1 )^2\equiv 1\pmod{13}$$ $$(\pm2 )^2\equiv 4\pmod{13}$$ $$(\pm3 )^2\equiv 9\pmod{13}$$ $$ (\pm4 )^2\equiv 3\pmod{13}$$ $$(\pm5 )^2\equiv {-1}\pmod{13}$$ $$(\pm6 )^2\equiv 10\pmod{13}$$Which shows that the solutions to $x^2\equiv 1\pmod {13}$ are $\pm1$.  Thus, I concluded that the solutions to $x^2\equiv 1\pmod {91}$ must be $\pm1$. I thought that $\pm1$ were the only solutions, but apparently I am incorrect! How do I go about finding the other solutions to this congruence? What's the right course of action for cross-site duplicates?  There are two flavors:   A question is posted which belongs on another site and ends up already having been asked there. I can't find an example right now, but it's bound to happen soon if it hasn't already. The same question is posted in two places at the same time. Take  for example, which is a duplicate of , posted within a half hour of each other by the same user.   Possible actions:   Move it to the proper site and close it once it gets there as a duplicate. Provide a way to close it right away as a cross-site duplicate, without moving it first. Flag it and let a moderator merge them. Close it as "no longer relevant" or something else.   Additionally, flavor 2 is a bit of a special case; perhaps the question really spans both sites in terms of content and intended audience. Should multiple-postings in this case be allowed? If so, should they somehow be linked to each other? If not, how do we avoid a migration war? How to listen my local FM stations in my iphone 4? Like I can listen with my old Nokia phone, without using Internet, GPRS etc.  Is iPhone 4 lacking this facility?  I heard about "Pandora Radio" but it uses the Internet to run and it's also not for Indian FM channels.  In my Nokia Express Music Mobile I can listen my local FM stations without any GPRS, Internet in mobile.