I know these two phenomena but I want to know a little deep explanation. What type of fringes are obtained in these phenomena?
Why is it difficult to differentiate between  and ? Is it because we don't clearly understand how both of these phenomenon takes place?   My thoughts: From an answer to one of my earlier question  I could understand that light waves behave differently when it strikes a slit which is of several times bigger than its wavelength and when it strikes a slit of size comparable to it its wavelength.In the former case the different points on the slit acts as wave-front sources producing circular wave fronts which interfere to form the diffraction pattern but in the later case plane wave-front striking a slit after passing through it forms circular wave-fronts and two such wave-fronts from two different slits interfere to form the interference pattern. But, I'm not satisfied by that because I don't get any intuition about points on the slit acting as wavefront sources. So, what is actually happening?
What does the notation $\Gamma \vDash \phi$ mean (in Mathematical Logic)? What does the notation $\Gamma \vDash \phi$ mean (in Mathematical Logic)?  I understand that $\Gamma$ represents a system of formulas, and that $\phi$ represents an individual formula.  I also know that $\Gamma \vDash \phi$ means " $\phi$ is a semantic consequence of $\Gamma$" - but I do not understand what this actually means. Can someone explain this idea to me in layman's terms?  Furthermore, suppose I had the following question:     Let $\Gamma \cup \{ \phi \}$. Does $\Gamma \vDash \phi$ hold for the set of formulae   $$ \Gamma = \{ p \rightarrow q, q \rightarrow r, r \rightarrow s \} \hspace{10 mm} \text{ where } \phi \text{ is } p \rightarrow s $$   Would I attempt this question by trying to prove that, for every formula $\psi \in \Gamma$, the valuation $v(\psi) = T$, based on the assumption that $v(\phi) = T$? I’m able to copy-paste from any application to any application. I’m able to copy from a comment or from a question or from an answer. I’m able to paste to a question or answer. However, if I attempt to paste into a comment, nothing happens. I am able to subsequently paste into another application, confirming that the text is actually on the clipboard.   However, copying SE links will paste them successfully, but all other text - including other links - still fails. This leads me to believe that it’s a SE issue and not an Apple one.   This has been an issue since 11.0 beta and persists through iOS 13 release. Label equations arbitrarily How do you reset timers? I tried out the clock setting cheat on a throw-away vault but somehow it also messed up my real one so now they both have 3000+ hours on radio station and 70d+ on returning wastelanders..   Any way to reset all the timers to default?  For some reason my phone refuses to change time at all anymore.. Remove default ID attribute from HTML helpers in ASP.NET MVC Examples in which the light maximizes the optical path length I posted a similar  about geodesics on Math.SE. Many sources ( for instance) claim that the light could maximize the optical path length in some cases. But I don't think it's actually true since between two points I can always imagine a path with arbitrary length. Therefore, or the light minimizes the optical length or it's stationary (neither maximum nor minimum). My question is: is the trajectory in red in the figure below a local minimum or a stationary curve?   If I'm wrong, please provide some examples which the light propagates in trajectory of maximum length. How does the secondary effect of the Heat Metal spell work? The  spell description states:  If a creature is holding or wearing the object and takes the damage from it, the creature must succeed on a Constitution saving throw or drop the object if it can. If it doesn't drop the object, it has disadvantage on attack rolls and ability checks until the start of your next turn...  I am unsure how this disadvantage mechanic functions as a whole. When do you suffer from it and in what ways (if any) can you end it? For example: What happens if you fail the save but cannot drop the object? Does dropping the object later, on your turn, do anything? What happens if you succeed on the save?  Does dropping the object later, on your turn, do anything? I would like it to be assumed that ; however, heat metal can still force you to drop the weapon. I would also like it to be assumed that . Model a simple 3D spiral shape? I need to model a simple spiral shape. I imagine the best way to do this is with curves, but I am unsure how to create a perfect spiral shape with curves. What's the best/easiest way to make a spiral tube? Wire nut several wires together I need a wire nut large enough so that I can bundle seven 14 gauge neutral wires together. I am trying to splice it so I can connect it to my new smart wifi leviton light switch.  I don't know which wire nut size to buy.  The boxes say for example: minimum 2#14 gauge - maximum 2#10 gauge.   My question is, can you tell me which wing nut or brand or size to buy so I can group 7 neutral wires together? None of the sizing chart on the box says the exact words of "ok to bundle seven #14 gauge wires together.  Which one should I use? Let $R$ be a commutative ring with identity. Show that $R$ is a field if and only if the only ideals of $R$ are $R$ itself and the zero ideal $(0)$.  I can't figure out where to start other that I need to prove some biconditional statement. Any help? postfix doesn't work after iptables set up This is almost a duplicate of the following questions (but, read further):      But, I wasn't able to apply the proof to my case of a group of order 10 and an element of order 5.  In my case, if I try a proof by contradiction, I'm left with the fact that every element in $G$ is of order 2, but if I divide them into subgroups, every subgroup is of order 2, and has one unique element.  I also tried other methods to prove the theorem, but couldn't come up with anything meaningful.  I'm a beginner in the field, and am not familiar with theorems such as Cauchy's or Sylow's theorem (I'm aware of Lagrange's theorem). Therefore, please try to provide a simple answer, thanks! Possible Duplicate:        My Windows 7 is 64-bit, and I thought that means it can use the full 4GB of RAM installed on the computer.  But I just saw this on my computer's properties: (So only 3.25GB is usable??) How to let PHP to create subdomain automatically for each user? How do I create subdomain like  ? Do i have to access htaccess somehow? Is it actually simply possible to create it via pure php code or I need to use some external script-server side language?  To those who answered: Well, then, should i ask my hosting if they provide some sort of DNS access?? Background  My Lenovo X250 is arriving in two weeks, which according to  will work well only with "a special image of Ubuntu pre-installed by the manufacturer."   points out that the X250 has "Excellent" compatibility to the Linux OSes they install. On the other hand, a quick search on  or  shows that a standard image of Ubuntu on the X250 is rife with hardware problems.  Ubuntu Certified Hardware acknowledges this for the X250: "Standard images of Ubuntu may not work at all on the system or may not work well." This  clearly shows the difference between an Ubuntu standard image installation and the one that comes pre-installed by the manufacturer. Hardware seems to work fully on the OEM version.  Question  Any idea where we may access or download these "special images of Ubuntu"?  (Hopefully not only for the X250, but also for the other systems out there.) Hanging indent inside list I would like items in a list to have a hanging indent (that is, for all lines after the first to be indented by a space or more),  but the traditional \hangindent command doesn't work for this.  \documentclass{article}  \begin{document} \hangindent=1cm This line of text has a hanging indent that looks fine, as long as it is outside a list environment. \begin{enumerate} \item \hangindent=1cm This line is inside a list environment and doesn't have a hanging indent- how can I add one? \end{enumerate} \end{document}     How can I add a hanging indent within a list? Complex polynomial of degree $n$ How to make terminal transparent while still having its own background image? Is there a way to give terminal specific background image and make it 50% transparent at the same time? How do I drill a 2⅛ inch door knob hole over an existing 1½ inch hole? I need to replace the door knob for this interior door:    The door knobs I've found at the stores require a 2⅛ inch hole.  Mine is only 1½:    Did door knobs used to be smaller?  Is there some place I can find a replacement door knob that will fit my door?  If I need to modify the door to fit a modern door knob, will the new hole completely overlap the old? and can I reuse the latch hole? What are integers $x$ and $n$ such as $ x^4+x^3+x^2+x+1 = n^2$? What are the integer numbers $x$ such as $x^4+x^3+x^2+x+1$ is the square of an integer?  $0$ and $-1$ are obvious answers, but how many are there?