Is there any mathematical proof to show that the exposure in a camera is independent of the focal length used, if the f-number (ratio of focal length to lens diameter) remains constant?
I'm trying to wrap my head around the math/physics of how illuminance on the film/sensor plane remains equal for a given f-number regardless of the focal length of the lens.  Since a longer lens will have a larger entrance pupil at a given f-stop than a shorter lens at the same f-stop, how can the light falling on the film/sensor be equivalent?  Empirically, I know this to be true.  Say I take an incident meter reading (not reflected/TTL) off my subject, and get f/5.6 at 1/100s, I'll get proper exposure at the point at which i took the meter reading with that setting whether I use a 50mm lens or a 200mm lens (obviously composition will be different).    Wikipedia's  reads:     A 100 mm focal length f/4 lens has an entrance pupil diameter of 25   mm. A 200 mm focal length f/4 lens has an entrance pupil diameter of   50 mm. The 200 mm lens's entrance pupil has four times the area of the   100 mm lens's entrance pupil, and thus collects four times as much   light from each object in the lens's field of view. But compared to   the 100 mm lens, the 200 mm lens projects an image of each object   twice as high and twice as wide, covering four times the area, and so   both lenses produce the same illuminance at the focal plane when   imaging a scene of a given luminance.   I'm not sure I agree with the explanation on wikipedia.  The film/sensor doesn't care how big the image is that falls outside the bounds of the sensor; the film/sensor "sees" what it sees, and that's it.
I've read and have heard of both 'as per' and 'per' being used conversationally, both with the same connotation of either 'according to' or 'on authority of'  Examples:  "Tell Ron to start molding new rollers for the mecanum wheels, as per me"  "Per Mr. Crane, you need to start the molds for the new rollers."  They both establish the same context by setting that something should be done on the authority of someone else (or the speaker, per the first example (see what I did there?)). Or it acts as a way to cite a source of a statement, directive or fact in conversational speech.  My question is, what is, if any, the functional and syntactical difference between as per and per. If there are no differences, which is apropos to use? Elevating process privilege programmatically? I'm trying to install a service using InstallUtil.exe but invoked through Process.Start. Here's the code:  ProcessStartInfo startInfo = new ProcessStartInfo (m_strInstallUtil, strExePath); System.Diagnostics.Process.Start (startInfo);   where m_strInstallUtil is the fully qualified path and exe to "InstallUtil.exe" and strExePath is the fully qualified path/name to my service.  Running the command line syntax from an elevated command prompt works; running from my app (using the above code) does not. I assume I'm dealing with some process elevation issue, so how would I run my process in an elevated state? Do I need to look at ShellExecute for this?  This is all on Windows Vista. I am running the process in the VS2008 debugger elevated to admin privilege.  I also tried setting startInfo.Verb = "runas"; but it didn't seem to solve the problem. How do I get the first element from an IEnumerable in .net? I often want to grab the first element of an IEnumerable&lt;T&gt; in .net, and I haven't found a nice way to do it.  The best I've come up with is:  foreach(Elem e in enumerable) {   // do something with e   break; }   Yuck!  So, is there a nice way to do this? My problem is we want to minimize $1/2 \cdot \text{Norm}(w)^2$ under suitable constraints $y(i){[w^Tx_i+b]-1}$.  We write the Lagrangian and get the above equations.  I have a problem in differentiating with respect to $w$ can somebody elaborate on that? How do we get first equation? What does "yield break;" do in C#? I have seen this syntax in MSDN: , but I don't know what it does.  Does anyone know? Setting time limit php Should searching by default be AND or OR? On my website I have a search bar.  It's powered by Lucene.net.  I have a requirement to make search be a substring case insensitive search, with direct hits appearing before substrings.  What I don't know, however, is when a user searches for a multi-word item--say "Chocolate Milk"--should that be treated under the hood as an AND or OR search?  As an example:  *chocolate* AND *milk*   vs  *chocolate* OR *milk*   The requirement right now is to treat this as an AND, but I'm not sure if that's the right way to go about it.  What would be the best in terms of UX?  I would think the best thing to do would be an OR search, with items containing both keywords appearing before items containing only one of the keywords.  Thoughts?  EDIT: The types of items being searched are medical supplies, with very cryptic names. Is it just that nvarchar supports multibyte characters? If that is the case, is there really any point, other than storage concerns, to using varchars? Is there a HTML opposite to ? Is there a tag in HTML that will only display its content if JavaScript is enabled? I know &lt;noscript&gt; works the opposite way around, displaying its HTML content when JavaScript is turned off. But I would like to only display a form on a site if JavaScript is available, telling them why they can't use the form if they don't have it.  The only way I know how to do this is with the document.write(); method in a script tag, and it seems a bit messy for large amounts of HTML. C++ STL Vector Iterator accessing members of an Object I think I've declared a Vector with an object correctly.  But, I don't know how to access it's members when looping with Iterator.  In my code, the line --->>  cout &lt;&lt; " " &lt;&lt; *Iter;  How do I print the contents of the members?  Like *Iter.m_PackLine ???  Not sure if I used the correct terminology, but appreciate the help!  Thanks  class CFileInfo {   public:       std::string m_PackLine;       std::string m_FileDateTime;       int m_NumDownloads; };  void main() {   CFileInfo packInfo;    vector&lt;CFileInfo, CFileInfo&amp;&gt; unsortedFiles;   vector&lt;CFileInfo, CFileInfo&amp;&gt;::iterator Iter;    packInfo.m_PackLine = "Sample Line 1";   packInfo.m_FileDateTime = "06/22/2008 04:34";   packInfo.m_NumDownloads = 0;   unsortedFiles.push_back(packInfo);    packInfo.m_PackLine = "Sample Line 2";   packInfo.m_FileDateTime = "12/05/2007 14:54";   packInfo.m_NumDownloads = 1;   unsortedFiles.push_back(packInfo);   for (Iter = unsortedFiles.begin(); Iter != unsortedFiles.end(); Iter++ )  {     cout &lt;&lt; " " &lt;&lt; *Iter; // !!! THIS IS WHERE I GET STUMPED     // How do I output values of the object members?   } }  // end main Can a 3rd party charger damage my macbook pro? I am a Bangladeshi citizen. Back in 2013, I went to India with a tourist visa and overstayed for four days. It was due to a gout attack in my feet but I don't have my medical papers to prove that.  I applied again in 2015 for a visa, at Dhaka, and they refused my visa and blacklisted my passport, writing some numbers and date on it. Now I am not able to get an Indian visa.  How I can remove my passport from the blacklist and get a new Indian visa? Do I need a Indian immigration lawyer to do this? Find $\space\ \begin{align*} \lim_ {x \to+\infty} \left [ \frac{\log_{2}(x-1)}{x}\right]   \end{align*}$.   After some minutes around this limit I did it this way:  $\log_{2}(x-1)=y \Leftrightarrow 2^y=x-1$  So,$\space x=2^y+1$.  When $x \to +\infty$,$\space y \to +\infty$ also. By substitution:  $\begin{align*} \lim_ {y \to+\infty} \left [ \frac{\log_{2}(2^y+1-1)}{2^y+1}\right]=\lim_ {y \to+\infty} \left [ \frac{\log_{2}(2^y)}{2^y+1}\right]=\end{align*}$  $\begin{align*}\lim_ {y \to+\infty} \left [ \frac{y}{2^y+1}\right]=\lim_ {y \to+\infty} \left [ \frac{1}{\frac{2^y+1}{y}}  \right]=\lim_ {y \to+\infty} \left [ \frac{1}{\frac{2^y}{y}+\frac{1}{y}}\right]= \frac{1}{+\infty+0}=0  \end{align*}$  Is this correct?Are there any other easy way to find this limit?Thanks I am technically knowledgeable enough to know that this most likely isn't possible, BUT, I am curious just the same (it must be put to rest). Is there anything preventing us from creating a means to use two different internet connections, like two different ethernet cards or an ethernet card and a wireless card, and using the two IP addresses at once for more internet speed?  My specific situation is that I would like to use both a wireless card and my wired connection on my machine running Kubuntu 13.10. Using two internet connections would allow me to do things like:   Torrent and browse simultaneously without lag Open Firefox with multiple tabs faster (?) Download a couple or a few large files at once double time Increase overall internet connection speed (?) Expressing $1.24\overline{123}=1.24\;123\;123\;123\;\ldots$ as the ratio of two integers Force update from unsigned repository I'm using an unsigned repo in Ubuntu 16.04 from Debian multimedia:  deb http://www.deb-multimedia.org jessie main   To install deb-multimedia-keyring, I'm running:  apt-get update &amp;&amp; apt-get install deb-multimedia-keyring -y   This gives an error:  W: GPG error: http://www.deb-multimedia.org jessie InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 5C808C2B65558117 E: The repository 'http://www.deb-multimedia.org jessie InRelease' is not signed. N: Updating from such a repository can't be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details. Include the "People Reached" and "Helpful Flags (count)" data in SEDE SSH Server stops working after reboot, caused by missing /var/run/sshd Volume of bounded region between sphere and a plane Understand PAM and NSS In the last days I have set up some Linux system with LDAP authentication and everything works fine, but there's still something I can't really understand regarding NSS and PAM, also after a lot of research. Citing:  NSS allows administrators to specify a list of sources where authentication files, host names and other information will be stored and searched for  and  PAM is a set of libraries that provide a configurable authentication platform for applications and the underlying operating system  What I don't understand is how PAM and NSS work and interact together. In  the architecture is explained pretty well: I configure PAM to use pam_ldap for LDAP accounts and pam_unix for local accounts, then I configure nsswitch.conf to fetch information from local files and LDAP. If I have understood correctly LDAP is used twice: first by pam_ldap and then by NSS which is itself called from pam_unix. Is that right? Is LDAP really used twice? But why do I need to configure both NSS and PAM? My explanation is that PAM performs different tasks than NSS and it is used by other programs. But, then, it should be possible to use only NSS or only PAM, as I have read in . So I experimented a bit and I have first tried to delete LDAP from the nsswitch.conf (and the authentication stopped to work as if only pam_ldap is not enough to do the job). Then I re-enabled LDAP in NSS and I deleted it from the PAM configuration (this time everything worked fine, as if pam_ldap is useless and NSS is enough to authenticate a user). Is there anyone who can help me to clarify this? Many thanks in advance. UPDATE I've just tried something now. I removed again all the pam_ldap entries in all pam configuration fields and I have also removed shadow: ldap from nsswitch.conf. As now in all the system there are only the lines: passwd: ldap files and group: ldap files in nsswitch.conf. Well... the login with LDAP users works perfectly, those two lines (plus /etc/ldap.conf) are enough to configure LDAP auth. From my knowledge PAM in independent from NSS, but my tests showed it's not. So I ask myself is it possible to completely disable NSS and use only PAM?