I wanted to make a magnifying glass in blender. I added in a circle and gave it a little thickness. Gave it a casual glass shader too. But all I got was this:   There is no magnification at all. Does anyone know how to make a lens that actually magnifies ? I would also like to know how to control the power of the lens. EDIT- I understand that you need a curved surface for the bending of light but how do I make a curved lens? I'm newbie to blender sorry if this question sounds stupid.
I'm fairly new to blender and not a graphics person by any stretch of the imagination. I've been having some success though modelling semi-reflective glass for a project I wish to build (physically) and I'm wondering if it is possible to model the effects of a lens. The lens I wish to model is a double-convex type. It has a diameter of 120mm and a focal-length of 301mm. Is this something that can be modelled in blender and if so, how? I'd like to be able to position the camera close to this lens and reproduce the magnifying effects of the lens on the scene behind the lens as well as depth-of-field effects.  Thanks a lot.
"the Red Cross" but no article in Greenpeace, UNICEF, or Amnesty International In an English language textbook for Italian middle school students, there is a reading exercise where students have to fill in the gaps. Here is a completed excerpt     The International Red Cross/Red Crescent is a global charity and humanitarian organisation. It believes that people everywhere have a right to life and health. …blah, blah, blah… The Red Cross / Red Crescent began its work in 1863. Today, it operates in 186 countries and every year it gives help to about 250 million people.    My two private students had to write a paragraph about a charitable institution of their own choice. We came up with 1. Médecins Sans Frontières (in Italian Medici Senza Frontiere) which is also known as Doctors Without Borders 2.  and 3. Amnesty International. They each chose an institution and they all started their paragraphs with the definite article "the" just like in the textbook.         The Doctors Without Borders is a global charity and humanitarian…   The Greenpeace is a global charity and pacific organisation…      I crossed out the articles and said they weren't needed. Samuele asked me why–good for him–but I didn't know what to say, so I promised I would look into it.  While I can explain that the definite article is needed when we mention the  because it is a collection of states/nations, and it is omitted when it is shortened to UNICEF. I don't know why the article is needed for the  but not for  or .   I'm also aware that if the name of a company or band starts with "The" e.g. The Beatles,  The Leathersellers’ Company, and The Body Shop  the article is always obligatory and always capitalised. However, the charity's name used in the book name is , and yet the article is needed.    Is there a reason? Why is the definite article necessary in the International Red Cross, but not for Greenpeace or Amnesty International? Modular Arithmetic - Find the Square Root The product of a normal and Rademacher variables, independent from each other Let $X\sim N(0,1)$ and let $Z$ be a random variable independent of $X$ such that:  \begin{equation} \Pr(Z=z) = \begin{cases} \frac{1}{2} &amp; \mbox{if $z = -1$ or $z=1$}, \\ \\ 0 &amp; \mbox{otherwise}. \end{cases} \end{equation}   Define $Y = ZX$. Show that $Y \sim N(0,1)$. Determine $\operatorname{Cor}(X,Y)$. Are $X$ and $Y$ independent?   Progress:  I'm basically stuck at the beginning. I got as far as $P(ZX &lt; y) = P(Z &lt; y/X)$, which I'm not even sure is correct. I'm also not clear on what it means by defining $Y = ZX$ - does it mean I need to state the probability density function or something? And how do I show that $Y \sim N(0,1)$? How to create dummy webcam? I would like to join some videoconference, but I don't own a webcam and the conference software requires one.  So my question is, can I create a dummy one? I don't care what the cam will cast, I just need to appear to have one. I have an application in C# (2.0 running on XP embedded) that is communicating with a 'watchdog' that is implemented as a Windows Service. When the device boots, this service typically takes some time to start. I'd like to check, from my code, if the service is running. How can I accomplish this? How to recover a dropped stash in Git? I frequently use git stash and git stash pop to save and restore changes in my working tree. Yesterday I had some changes in my working tree that I had stashed and popped, and then I made more changes to my working tree. I'd like to go back and review yesterday's stashed changes, but git stash pop appears to remove all references to the associated commit.  I know that if I use git stash then .git/refs/stash contains the reference of the commit used to create the stash. And .git/logs/refs/stash contains the whole stash. But those references are gone after git stash pop. I know that the commit is still in my repository somewhere, but I don't know what it was.  Is there an easy way to recover yesterday's stash commit reference?  Note that this isn't critical for me today because I have daily backups and can go back to yesterday's working tree to get my changes. I'm asking because there must be an easier way! How to mass rename files with ill-formed numbering? I've got bunch of files with ill-formed numbering:  prefix-#.ext       | for files with number 1-9 prefix-##.ext      | for files with number 10-99 prefix-###.ext     | for files with number 100-999   Due to further processing I need all of their names to be in format: prefix-###.ext. Is there any easy way to do that? Let $x\in \mathbb{R}$ an irrational number. Define $X=\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$. Prove that $X$ is dense on $[0,1)$.    Can anyone give some hint to solve this problem? I tried contradiction but could not reach a proof.  I spend part of the day studying this question   and its answers. Only one answer is clear and give clues to solve the problem. This answer is the first one. However, this answer does not answer the question nor directly, nor the proof follows from this answer.   This answer has some mistakes, he use that $[(k_1-k_2)\alpha]=[k_1\alpha]-[k_2\alpha]$ which is not true. Consider $k_1=3, k_2=1, \alpha=\sqrt{2}$ we have $[(k_1-k_2)\alpha]=2\not= 3=[k_1\alpha]-[k_2\alpha] $. We only can assure that $[k_2\alpha]-[k_1\alpha]-1\leq [(k_2-k_1)\alpha]\leq[k_2\alpha]-[k_1\alpha]$.   Who answered said something interesting about additive subgroups of $\mathbb{R}$, but unfortunately the set $X=\{nx-[nx] : n\in \mathbb{N} \}$ is not a subgroup. Considering the additive subgroup $G=\langle X \rangle$, if we prove the part (a) of the link, we get that indeed $G$ is dense on $\mathbb{R}$ but we can not conclude that $X$ is dense on $[0,1)$.  I think this problem has not been solved.  Thanks! Thousands of .log files in Exchange 2007 Server folder I'm a bit of an Exchange admin noob so I don't know if this is normal, but on our Exchange 2007 server under C:\Program Files\Microsoft\Exchange Server\Mailbox\First Storage Group\ there are 30,000 1MB .log files.  I don't know if those should be there or not, but they keep multiplying like little jackrabbits.  I've so far resisted deleting them as I'm sure something would break, but it's come to the point now where our 80GB disk is completely full up and Exchange has stopped receiving messages.  My best guess is that these are transaction logs and would be useful in rebuilding the database should something go awry, but 30GB of transaction logging seems a bit excessive.  Is there a way to limit it or is that even a good idea?  And of course did I completely miss the point? If I play a spell with {X} in the mana cost, and I have a card out that reduces the casting cost by 2 generic mana, what happens to the X? Does it start at -2?  For example: I have  in play. If I play  for just 1 blue mana, do we draw 2 cards? I have a server running with the timezone set to UTC. It seemed like that was generally a good practice (please correct me if I'm wrong).  Anyhow, one of the servers I connect to, in order to scp files, is running on EDT and stores files that I need to copy in the format /path/to/filename/data20120913  I looked at trying to rsync files using something like find's -mtime -1 flag for files modified in the last day, but I didn't have any luck.  I don't mind just using scp to copy the current day's file, but as of right now there is a 4-hour window where running date +%Y%m%d will give a different day on each server and that bugs me a little.  Looking through man date I see that I can have the time output as UTC, but I don't see a way to have it output as another timezone like EDT  I suppose I could also use something like the GNU date extension date -d 20100909 +%s to get the date in seconds from the epoch, apply a manual 4 * 60 * 60 second calculation, and see about rendering that as a date - but then when daylight time kicks in it will still be an hour off.  Is there a simpler way to output the date in a YYYYMMDD format for EDT on a server that is set to UTC ? How to find historical airfares? Is there a way to find out how much it would have cost to buy a particular airplane ticket at some point in the past?    For example, how could I find out how much it would have cost to buy a one-way itinerary from airport A to airport B on October 1, 2011 for travel on November 1, 2011? Frying Oil Reuse What are some guidelines or rules with regard to filtering and reusing (vegetable/canola/sunflower) oil that has been used for deep frying?  Is it safe and acceptable under some circumstances to filter and keep oil? If so, does it depend on which foods were fried? How long can the filtered oil for be kept for?  Or, is it never appropriate? If not, are the reasons health or flavour related? or both? No sound from speakers on MacBook Pro except the startup chime After plugging my headphones out, suddenly there is no sound from the internal speakers. When I press volume buttons, I see a circle-backslash symbol below the speaker icon.  Restarting doesn't help. However I do hear the startup chime. What should I do? Localization of a UFD that is a PID SSH to open GUI on target machine? I am a beginner in learning selenium Webdriver. I am not able to understand how page object and factory models works and how it can be beneficial?    Kindly help me explain it with detailed explanation. How are PCA and classical MDS different? How about MDS versus nonmetric MDS? Is there a time when you would prefer one over the other? How do the interpretations differ? I'm trying to make airsoft chronograph/chronometer (a device that measures airsoft bullet speed). The idea is to measure time in which bullet is traveling from point A to point B, and then I can calculate bullet speed. Bullet is shot into plastic pipe with diameter of 32mm. I've tried to put on one side IR LED and on the other side phototransistor (BPW 40), both at the start and end of the tube. Something like this:  Blue circles are phototransistors, red circles are IR LEDs and white circles are airsoft bullets. When bullet passes through area where bullet 2  is drawn (just in between IR LED and phototransistor), everyting works perfectly. But when the bullet passes where bullets 1 and 3 are drawn, it isn't detected. That is expected, but unwanted behavior. So my question is: how can I detect bullets regardlessly of it's position ? I've thought about putting IR LEDs and phototransistors around the pipe (not only in one place), like this:  but this solution isn't cheapest: 5 IR LEDs + 5 BPW 40 = cca $12 times 2 (because I need it on both sides of the pipe) = $24. Is there any cheaper solution ? Is BPW 40 good choice for phototransistor ? I don't know which IR LEDs I'm using (and salesman in the store also doesn't know - he told me these are generic ones for remote controllers, like TV or DVD controller). Diameter of the pipe is 32mm and it will be long about 14cm (sensors will be 10cm apart). Diameter of airsoft bullet is 6mm. EDIT: I'll go for my second idea. I just have one more question: is it better to arrange IR emitters and photo transistors this way:  or this way:  Thanks !! A contractive mapping on $M$ is a function $f$ from the metric space $(M,d)$ into itself satisfying $$d(f(x),f(y))&lt;d(x,y)$$ whenever $x,y\in M$ with $x\ne y$. Prove that if $f$ is a contractive mapping on a compact metric space $M$, there exists a unique point $x\in M$ with $f(x)=x$.   Consider the function $g(x)=d(f(x),x)$. Note that   \begin{align*}d(f(x),x)-d(f(y),y)&amp;\leq (d(x,y)+d(y,f(x))-(d(y,f(x)-d(f(x),f(y)) \\ &amp;=d(x,y)+d(f(x),f(y)) \\ &amp;&lt;2d(x,y)  \end{align*}  And similarly for $d(f(y),y)-d(f(x),x)$, so we have $|d(f(x),x)-d(f(y),y)|&lt;2d(x,y)$. This means $g(x)$ is continuous.  So $g(x)$ is a real-valued continuous function on a compact space, so must be bounded and has a minimum $c$, i.e. there exists $x_0$ such that $d(f(x_0),x_0)$ equals the minimum $c$. What then?