If a light incident on a smooth surface ,then light reflects. Why does the reflected light goes in a direction such that angle of incidence and angle of reflection  to be equal and reflected ray be in the plane of incidence?  In short , why does the law of reflection hold true?  (I mean the plane of incidence here as the plane containing the incident ray and perpendicular to the surface of incidence)
In the Law of Reflection, the angle of incidence is equal to angle of reflection. Why is this true? This is clearly true experimentally, but how does one prove this true mathematically?
FTP client on windows that save session password in encrypted text Filezilla or WinSCP save password in plain text which is unsecured on public machines. Is there any FTP client can save and encrypt password so that people using it only can access to FTP but not able to see password? Thanks! Electrostatics and tv screens We have an Always On "cluster" that consists of 2 servers (there will be more), so one is PRIMARY and other(s) is(are) SECONDARY. The idea was to dedicate SECONDARY as a readonly replica, so it would be a somewhat search-server.  I do know how to set ConnectionString in the C# so it will use SECONDARY replica - just add ApplicationIntent=ReadOnly.  But I don't understand how to address the SECONDARY from stored procedure if I'm using distributed query. Is there a way to set some parameters to the query (like WITH statements or something), so query would use only replica and not the PRIMARY node?  The thing is, obviously from the start server1 is PRIMARY and server2 is SECONDARY, but when server1 fails then server2 is PRIMARY and server1 will be SECONDARY after it get fixed. So I cannot just use the static server2's name.  So far I've managed to get current replica's server name as a variable and use it in EXEC:  -- find first available replica DECLARE @replicaServer nvarchar(50)  SELECT TOP 1     @replicaServer = RCS.replica_server_name FROM     sys.availability_groups_cluster AS AGC     INNER JOIN sys.dm_hadr_availability_replica_cluster_states AS RCS           ON RCS.group_id = AGC.group_id     INNER JOIN sys.dm_hadr_availability_replica_states AS ARS           ON ARS.replica_id = RCS.replica_id     INNER JOIN sys.availability_group_listeners AS AGL           ON AGL.group_id = ARS.group_id WHERE ARS.role_desc = 'SECONDARY'       AND connected_state = 1  -- and query it DECLARE @cmd nvarchar(MAX) = 'SELECT * FROM [' + @replicaServer + '].[somebase].[someschema].[sometable]' EXEC (@cmd)   But that's a shame, I guess. How to label using just numbers from start of text field? Why do I get (author?) when I use \citet with natbib? I would like to show the author names using \citet but I get just the reference number. Here is a minimal code:  \documentclass{report} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage{natbib}  \begin{document}   The author \citet{toschi09} has shown that ..  \bibliographystyle{plain} \bibliography{foo}  \end{document}   And here is foo.bib  @article{toschi09, author = {Toschi, F. and Bodenschatz, E.}, title = {Lagrangian Properties of Particles in Turbulence}, journal = {Annual Review of Fluid Mechanics}, volume = {41}, number = {1}, pages = {375-404}, year = {2009},  }   What I get is:     The author (author?) [1] has shown that ..   Any help will be more than welcome, thank you! Why do stars flicker? Why do stars flicker and planets don't? At least this is what I've read online and seen on the night sky. I've heard that it has to do something with the fact that stars emit light and planets reflect it. But I don't get it, isn't this light, just "light"? What happens to the reflected light that it doesn't flicker anymore?  I was thinking that it has to do something with Earth's atmosphere, different temperatures or something (if this has any role at all). Lost/Deleted dpkg (package manager for Debian). How do I get it back? power outage/frozen meat We were on vacation for a week. The neighbor said we were out of power the whole time.  We have a chest freezer full of beef. It thawed but remained in the freezer unopened the whole time. Is the meat bad if it is thawed but still cold? Can we refreeze it and eat it? Show that $\sum_{n = 1}^{+\infty} \frac{n}{2^n} = 2$ Convert LaTeX to HTML Is there a converter that will convert LaTeX to HTML? I have tried several services but the LaTeX diagrams and some of the maths came out weird.  I actually converted the Latex to PDF without a problem. Then I used  to convert from PDF to HTML. The square root signs did not appear properly and some of the Cartesian coordinate plane diagrams had nothing on them except the grid.   \documentclass[12pt,a4paper]{report} \usepackage{amssymb} \usepackage{amsthm} \usepackage{amsmath} \usepackage{pstricks,pst-plot} \usepackage{pst-eucl} \addtolength{\hoffset}{0.2cm} \addtolength{\textwidth}{1.1cm} \addtolength{\textheight}{1.0cm} \addtolength{\voffset}{-0.7cm} \linespread{1.3} \begin{document}  If $x$ is non-positive then $x \leq -\sqrt{\frac{1}{2}}$     $\hspace{30 mm} $     (6)\\  (4) and (6) tell us that\\  (4)  $-1 \leq x \leq 0$  \\  (6)  If $x$ is non-positive then $x \leq -\sqrt{\frac{1}{2}}$\\  Therefore $-1 \leq x \leq -\sqrt{\frac{1}{2}}$\\  \vspace{50 mm}  \begin{align*} \psgrid[unit=2cm](0,0)(-2,-2)(2,2) \pnode(-1.8,.87){b}\uput[50](b){b} \pnode(-1.8,1.8){a}\uput[50](a){a} \psset{linecolor=green} \psline[linewidth=1pt](-1.8, 0)(-1.8,4) \psset{linecolor=green} \psline[linewidth=1pt](-1.8, 0)(-1.8,-4) \psset{linecolor=blue} \psellipticarc(0,0)(2,2){0}{180} \psset{linecolor=red} \psline[linewidth=1pt,linestyle=dashed,dash=2pt](-2,2)(-1.41,1.41) \psset{linecolor=red} \psline[linewidth=1pt](-1.41,1.41) \psset{linecolor=red} \psline[linewidth=1pt]{-&gt;}(4,-4) \psset{linecolor=red} \psline[linewidth=1pt]{-&gt;}(-2,2)(-4,4) \end{align*}  \end{document}   PDF output:    PDF->HTML output: Can I nohup/screen an already-started process? Which serial protocol or encoding scheme does this scoreboard use? I am trying to decode a signal stream coming from a Nevco scoreboard controller:    Packets like this are sent every ~2.7 ms.  I suspect it is some sort of UART signal because it is on the RX line of a ATMEGA48, but I cannot identify the finer protocol details like parity and stop bits. All the combinations I have tried returns junk data, so it may be another encoding scheme.  What's unusual is that the same signal is also sent to the MOSI pin of the microcontroller, but there is no clock signal anywhere.  A .vcd file is .   The shortest pulses (both high and low) are always 8us in length.    This is what two packets look like. Anyone got ideas? Agreeing on a single shortened nomenclature? I've noticed across various stack exchange sites that when they refer to their own stack exchange on their site, they'll shorten the name to something similar to either:  EE.SE (Electrical Engineering Stack Exchange) OR Tex.Sx (LaTeX Stack Exchange)  Essentially they'll do XX.SE or XX.SX which has the possibility to generate some confusion for new users.    Have I not visited enough sites and just noticed an outlier or would it be beneficial for Stack Exchange sites to agree on a shortened name nomenclature? How does Salesforce SSO call just-in-time handler methods Shutdown button only logs out ubuntu 15.04 How to prove the midpoint of a chord is also the midpoint of the line segment defined by the points of intersection of other two chords with it? Bernhard Elsner, alias MathOMan, posted this exercise in plane Geometry,  on January $29$th, $2010.$  "Let $\mathcal{C}$ be a circle, $A,B$ two distinct points on $\mathcal{C}$ and $M$ be the midpoint of the chord $[AB]$. Take two other chords,$[PQ]$ and $[SR]$, that pass through $M$. Let $C$ (resp. $D$) be the intersection of $[AB]$ with $[PS]$ (resp. $[RQ]$). Prove that $M$ is the midpoint of the chord $[CD]$."    To prove it I've written the following (failed) argument, in the  of this post (translation of mine):    The figure is symmetric with respect to $M$: $\overline{AM}=\overline{MB}$, $\overline{PM}=\overline{MU}$, $\overline{RM}=\overline{MW}$, $\overline{QM}=\overline{MV}$, $\overline{QR}=\overline{VW}$, $\overline{SM}=\overline{MT}$. From $\dfrac{\overline{SC}}{\overline{DT}}=\dfrac{\overline{CM}}{\overline{MD}}=1$ follows that $\overline{CM}=\overline{MD}$.  Here is an extract of the author's reply (translation of mine):   "It is not clear that  $\overline{QM}=\overline{MV}$. Is the point $V$ on the line $(QM)$ defined by this equality or is $V$ defined as the intersection point of the lines $(QM)$ and $(WC)$? Why are both definitions to give the same point?  Let $C^{\prime }$ be the intersection of $(SP)$ and $(VW)$, and $D^{\prime }$ the intersection of $(TU)$ and $(QR)$. (...)  One still has to show that $C^{\prime }=C$ and $D^{\prime }=D$."   I have agreed with these objections.  Until now no proof has been posted. The author considers that the "proof is not quite simple".  Q. What is the theorem this exercise refers to? Or how does one prove it? How do I block unwanted callers without jailbreaking? Paper status changed to “Decision in Process” rapidly after initial submission Induction Proof that $x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1})$ This question is from [Number Theory George E. Andrews 1-1 #3].     Prove that $$x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+\ldots+xy^{n-2}+y^{n-1}).$$   This problem is driving me crazy. $$x^n-y^n = (x-y)(x^{n-1}+x^{n-2}y+\dots +xy^{n-2}+y^{n-1)}$$  $(x^n-y^n)/(x-y) =$ the sum for the first $n$ numbers and then I added $(xy^{(n+1)-2}+y^{(n+1)-1})$ which should equal $(x^{n+1}-y^{n+1})/(x-y)$ but I can't figure it out    This is a similar problem in the book and I tried this method but it wasn't working out      $\quad$Thereom $\bf1$-$\bf2$: $\,\,\,\,$ If $\,x$ is any real number other than $1$, then $$\sum_{j=0}^{n-1}x^j=1+x+x^2+\ldots+x^{n-1}=\dfrac{x^n-1}{x-1}.$$    $\quad$Remark: $\displaystyle\sum_{j=0}^{n-1}A_j$ is shorthand for $A_0+A_1+A_2+\ldots+A_{n-1}.$     $\quad$Proof: Again we proceed by mathematical induction. If $n=1$ then $\displaystyle\sum_{j=0}^{1-1}x^j=x^0=1$ and $(x-1)/(x-1)=1$. Thus the theorem is true for $n=1$.  $\quad$ Assuming that $\displaystyle\sum_{j=0}^{k-1}x^j=(x^k-1)/(x-1)$, we find that $$ \eqalign{ \sum^{(k+1)-1}_ {j=0}x^j &amp; = \sum^{k-1}_ {j=0}x^j+x^k=\dfrac{x^k-1}{x-1}+x^k \\ &amp;= \dfrac{x^k-1+x^{k+1}-x^k}{x-1}\\ &amp;= \dfrac{x^{k+1}-1}{x-1}. }$$   Hence condition $(\rm ii)$ is fulfilled, and we have established the theorem.    $\quad$Corollary $\bf1$-$\bf1$: $\,\,$ If $\,m$ and $n$ are positive integers and if $m&gt;1$, then $n&lt;m^n.$ I just learned about the Monty Hall problem and found it quite amazing. So I thought about extending the problem a bit to understand more about it. In this modification of the Monty Hall Problem, instead of three doors, we have four (or maybe $n$) doors, one with a car and the other three (or $n-1$) with a goat each (I want the car).  We need to choose any one of the doors. After we have chosen the door, Monty deliberately reveals one of the doors that has a goat and asks us if we wish to change our choice.  So should we switch the door we have chosen, or does it not matter if we switch or stay with our choice?  It would be even better if we knew the probability of winning upon switching given that Monty opens $k$ doors.