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A lot of textbooks and exam boards claim that light incident at exactly the critical angle is transmitted along the media boundary (i.e. at right-angles to the normal), but this seems to violate the principle of reversibility in classical physics.  How would a photon or ray travelling in the reverse direction "know" when to enter the higher refracting medium?  It can't know, so I conclude that such light is simply reflected?  Is this correct? What's the canonical way to check for type in Python? Why doesn't a commutator cause the rotation to reverse periodically or stop? I understand the field magnets attracting/repelling the armature/coil so that it turns one half-turn and then, because the commutator is turned, its contact with the brushes has switched sides, and the current goes in the opposite direction, reversing the electromagnetic polarity. Then, because the polarity is swapped, it attracts/repels to complete the second half-turn. The thing is, isn't it a bit of a gamble that it will turn in the same direction? Couldn't the it just be pulled/pushed back, more or less undoing the half-turn?  I'm also a bit confused how the rotation doesn't just stop once the commutator is oriented so that the brushes are contacting both sides of the commutator. In other words, there's a brief period just as the commutator switches the current directions where each both the brushes are in contact with both sides of the commutator where the current is neutralized. Shouldn't this stop the motor?    For reference, I'm just talking about a simple DC motor. I want to install Skype, but I can't locate it in Software Center or by using Synaptic Package Manager. Can anyone help me? When you energise a taut string, the following resonant modes of vibration occur:    Plotting on the frequency domain, you can see their corresponding frequencies:    But what is the underlying physical principle? Why does this happen?  Is there any way of explaining it that could be understood by a smart 15 year old?  EDIT: I'm going to give my best attempt so far. Here goes:   We can start with sympathetic resonance. Sounding a particular frequency, a pure sinewave.  And noticing the string resonates sympathetically at the frequency of each harmonic. Say this is explained and understood. Now imagine that plucking a string is equivalent to a burst of white noise, which contains frequencies all the way through the spectrum. This could be approached backwards, by starting with random frequencies and noticing that resultant wave produced looks like white noise.   If the above is scientifically correct, then it restricts the domain of the question.  I would really like to be able to understand it scientifically and also be able to explain it intuitively.  PS Images from Can there be a function that's even and odd at the same time? If $x$ and $y$ are irrational, is $x + y$ irrational? Is $x - y$ irrational? Named parameters in JDBC Why does exclamation mark within double quotes cause a Bash error? Please look at these commands:  $ notify-send SYNC TIME! $ notify-send 'SYNC TIME!' $ notify-send "SYNC TIME!" bash: !": event not found $   The first two commands produce a notification bubble as expected. The third gives the error shown.  and  $ echo SYNC TIME! SYNC TIME! $ echo 'SYNC TIME!' SYNC TIME! $ echo "SYNC TIME!" bash: !": event not found $   Here as well, the echo works for first two commands but not in the third.  More problems here (although I was not planning on using this): both notify-send "SYNC!TIME" and echo "SYNC!TIME" give bash: !TIME": event not found.  But both notify-send and echo work with "SYNC! TIME"  Can someone please explain why the bash: !": event not found error appears? When to use a linked list over an array/array list? I use a lot of lists and arrays but I have yet to come across a scenario in which the array list couldn't be used just as easily as, if not easier than, the linked list.  I was hoping someone could give me some examples of when the linked list is notably better. Why there is "the" before some names but not others Is there a rule beyond the common "no the with proper nouns and names" for the following problem?     I saw the Empire State Building.      We went to the White House.      We saw the Golden Gate Bridge.   but     I went to Death Valley National Park.      I crossed Brooklyn Bridge. How do I find the right size of filters for a lens? I was looking to get a circular polarizing filter and an UV filter for my Canon 550D, 18-135mm lens. When I checked online I found these filters came in different sizes, like 62mm, 67mm, 72mm, 77mm. How do I know which is right?  Also, will there be any degradation of photo quality if I put both these filters on the lens? Solenoid Driving Circuit I'm trying to drive a 12v (14W) solenoid and have problems figuring out the components for the driving circuit.  The solenoid draws about 1.166A and the MCU is being operated at 3.3V.  I've seen many driving circuits and they all look something like this:         &ndash; Schematic created using   My questions:   What datasheet parameters should I look for when designing this circuit? Is the IRF530PBF-ND a suitable MOSFET for driving this solenoid?    Also, how do I calculate R1's value?  I don't want to blindingly copy a circuit that may or may not work, I want to understand it.  Thank you so much in advance! Switching baselayers as user zooms in to map in OpenLayers? Elements of $\mathbb Q(2^{1/3})$ Is there some way to get explorer to generate thumbnails without actually having to navigate and scroll through every folder?  All I could get was a command prompt script that would load an explorer window for all subfolders, however only images that were visible would have thumbnails created. $\lim_{n\to\infty}a_nb_n=? $ given that $\lim_{n\to\infty}a_n=0$ and $\lim_{n\to\infty}b_n=\infty$ A. $\lim_{n\to\infty}a_nb_n=?$ given that $\lim_{n\to\infty}a_n=0$ and $ \lim_{n\to\infty}b_n=\infty$  B. $\lim_{n\to\infty}{a_n \over b_n}=?$ given that $\lim_{n\to\infty}a_n=0$ and $\lim_{n\to\infty}b_n=0$  C. $\lim_{n\to\infty}{a_n \over b_n}=?$ given that $\lim_{n\to\infty}a_n=\infty$ and $\lim_{n\to\infty}b_n= \infty$    These seem to be difficult situations I come across when I have to evaluate limits.   Some examples,    $\lim_{n\to\infty}n^a\sin(1/n^b)$ with $a,b&gt;1$   $\lim_{n\to\infty}{n^a\over \sin(1/n^b)}$ with $a,b&gt;1$   $\lim_{n\to\infty}{1/n^a\over \sin(1/n^b)}$ with $a,b&gt;1$   $\lim_{n\to\infty} nf(x_n)$ [where we only know that $\lim \ f(x_n) = 0]$    My first question is : Are the two situations  A and B  equivalent ? I feel that they are equivalent as $\lim_{n\to\infty}b_n=\infty \iff \lim_{n\to\infty}{1\over b_n}=0$, The problem is that I'm not sure if we can apply the product rule for limits to take the limit inside.  My second question is : What are some ways to solve such problems ? I only know that we can apply stolz- cesaro in some cases. How do I move Steam games to a new computer without re-downloading them? I have just bought a new computer and I have everything migrated over except for my Steam games.  I looked in Program Files/Steam/ and I found a folder full of the games I have downloaded, but I do not know if it is safe to just copy these folders from one computer to another (seeing as a lot of other applications will not work if you do this), or is there another recommended way?  I don't really feel like re-downloading all my games. I don't have the time nor bandwidth to download 20GB over a 1.5mbps connection.  Is it possible to contact Valve and get a disk with the games on it? Fourier series of Log sine and Log cos Why are continuous functions the "right" morphisms between topological spaces?