A 400mm f4.0 lens is supposed to have a maximum aperture diameter of 10cm. Looking at such a lens they don't seem big enough to fit that kind of aperture including all the mechanics for control inside them. Do modern lenses have a way of focusing light into a smaller aperture to behave like a bigger one or are they really always the size that the formula (fstop = focal length / aperture diameter) suggests?
I understand that the entrance pupil is the image of the aperture as seen from the front of the lens. However, is the size of the entrance pupil the same as the size of the effective aperture? In other words, if I measure the size of the entrance pupil by looking at it, will that be equivalent to the focal length of the lens divided by the f-number (with the focus set to infinity)? I know that sometimes this is hard to estimate because of the shape of the aperture blades, but I was wondering whether pupil and aperture can be quite different (perhaps at very low magnification).
Changing my iTunes account details How do I shrink the partition of an img file made from dd? Is the latest version of Ubuntu 100% FREE Run TTY script every time I open a GUI terminal Stack Overflow duplicated layer bug Number of elements in a finite $\sigma$-algebra Is your MAC address revealed when you hit up a website? When you hit up a site, such as cnn.com, does the TCP/IP packet contain the MAC address of your network card?  Could cnn.com theoretically record my MAC address? I have a problem understanding the proof of Rencontres numbers (Derangements) I understand the whole concept of Rencontres numbers but I can't understand how to prove this equation  $$D_{n,0}=\left[\frac{n!}{e}\right]$$  where $[\cdot]$ denotes the rounding function (i.e., $[x]$ is the integer nearest to $x$). This equation that I wrote comes from solving the following recursion, but I don't understand how exactly the author calculated this recursion.  $$\begin {align*}  D_{n+2,0} &amp; =(n+1)(D_{n+1,0}+D_{n,0}) \\ D_{0,0} &amp; = 1 \\ D_{1,0} &amp; = 0  \end {align*} $$ In  related question (), the OP asks if it is grammatical to use the definite article before phrases like Advanced programming in Java whitepaper and Microsoft Office 2010 product. The accepted answer by @Kosmonaut was:     Yes, it is. This is because the "Advanced programming in Java"   whitepaper phrase forms a syntactic unit, with whitepaper as the head   of the unit. The definite article for a phrase always corresponds to   the head of the phrase, so using the definite (or indefinite) article   for these phrases makes perfect sense and is correct English.   My question is whether the same answer applies to phrases like Heathrow Airport, Hyde Park,  Waterloo Station, Edgware Road and Parliament Square. I ask becase it seems to me that airport, park and station, etc. sound like they are part of the proper noun itself, and not simply a common noun. Moreover, I think the head of the unit in these cases would be the place name (first noun) and not the place type (second noun). If that's true, then I assume that no definite article should precede these phrases. Is that correct? I don't know so much about coordinate systems...  In my office we use to deal with spatial data coming from archaeological sites. Each site has its own x-y-z coordinate system (GCS). Three simple ortogonal cartesian axis. In the last years we have been managing this spatial data through GIS software (ArcGIS), without using specific coordinate system (just leave it as "undefined")  I'd like to know if there exisits any GCS designed to deal with such datasets using simple cartesian orthogonal axis, without grid distortions of the typical GCS. In addition, I'd like to know if this system is suitable for using it in an online mapping application.  By the way, we manage 2D (ArcMap) and 3D (ArcScene) environments and work with "mm" as length base unit.   If such a thing doesn't exists, maybe someone knows how to create it. Prove the following in $S_n$:  Let $\alpha = (a_1,a_2,\ldots,a_s)$ be a cycle and let $\pi$ be a permutation in $S_n$. Then $\pi\alpha\pi^{-1}$ is the cycle $(\pi(a_1),\ldots,\pi(a_s)).$     I'm not sure where to even start. How to change an input button image using CSS So, I can create an input button with an image using &lt;INPUT type=&quot;image&quot; src=&quot;/images/Btn.PNG&quot; value=&quot;&quot;&gt;  But, I can't get the same behavior using CSS. For instance, I've tried &lt;INPUT type=&quot;image&quot; class=&quot;myButton&quot; value=&quot;&quot;&gt;  where &quot;myButton&quot; is defined in the CSS file as .myButton {     background:url(/images/Btn.PNG) no-repeat;     cursor:pointer;     width: 200px;     height: 100px;     border: none; }  If that's all I wanted to do, I could use the original style, but I want to change the button's appearance on hover (using a myButton:hover class). I know the links are good, because I've been able to load them for a background image for other parts of the page (just as a check). I found examples on the web of how to do it using JavaScript, but I'm looking for a CSS solution. I'm using Firefox 3.0.3 if that makes a difference. Adding an error on a dynamic referenced field Is there a way to add an error on a dynamically referenced field? Let's take this simple example:  opp.get('Name').addError('Invalid name');   This is not working, I'm looking for a similar minded way.  Thanks divisibility of binomial coefficients by primes If $p$ is a prime number and $r = 1,2,3 \dots ,p -1$, how can I prove that the binomial coefficients $_nC_r(p,r)$ are divisible by $p$? By divisible I mean $_nC_r(p,r)/p$ leaves remainder $0$.  oivind Solving an equation over the reals: $ x^3 + 1 = 2\sqrt[3]{{2x - 1}}$ When in Demon Form, are demons vulnerable to mortal frailties? When a Demon is in Demonic Form, does he gain any intrinsic protection against mundane concerns like breathing or falling unconscious? In particular, when in Demonic Form do/are demons:  need to breath? immune to poisons? fall unconscious? (ie do they stay conscious on full lethal?) suffer from wound penalties for having damage in last 3 boxes? need to consume food/water? need to sleep?  The last two are only really a concern to demons who have burnt their last cover. However this can happen in play, and is pretty significant for any burnt NPCs. Is seems odd that a swarm of glass beetles clinging together into the shape of a man might have any issues with being poisoned. But I can't find it clearly stated, whereas it is clearly stated in Werewolf (the Forsaken). I currently have Windows 7 on my computer and I want to install Ubuntu alongside Windows safely.  Could someone please provide clear instructions? Is Ghost Adventures real or fake? 2-10x Slower Deployments with Winter '15? Navigation bar is too long on progressbar theme, can it wrap? My navigation bar at the top of each slide (that links to each section) has too many sections. I would like to keep the bar and keep each section but I would like to wrap it i.e. have it on two lines.  Is that possible?  I am using compress and I am using  as a theme.