Why is refraction of light at a boundary wavelength dependent, and are the two proportional? Just wondering, why is it that blue light will refract less than red light, i.e. why does the fact that blue light has a shorter wavelength mean that it will refract less at a boundary? I read somewhere that the wavelength decreases of light as it enters an optically denser material, which seems logical given that frequency remains constant and c = f λ. Is there some sort of constant which would mean that if the wavelength of a type of light in material one is x% shorter than that of, say, red light, the wavelength after refraction would be kx% shorter? I know this is a terribly worded question, this is all new to me and it's a bit difficult for me to put down my thought process. Thanks in advance!
Why do prisms work (why is refraction frequency dependent)? It is well known that a  can "split light" by separating different frequencies of light:    Many sources state that the reason this happens is that the  is different for different frequencies.  This is known as .  My question is about why dispersion exists.  Is frequency dependence for refraction a property fundamental to all waves?  Is the effect the result of some sort of non-linearity in response by the refracting material to electromagnetic fields?  Are there (theoretically) any materials that have an essentially constant, non-unity index of refraction (at least for the visible spectrum)?
Why aren't Java Collections remove methods generic? Why isn't  generic?    Seems like Collection&lt;E&gt; could have boolean remove(E o);   Then, when you accidentally try to remove (for example) Set&lt;String&gt; instead of each individual String from a Collection&lt;String&gt;, it would be a compile time error instead of a debugging problem later. Why does $F=ma$? Is there a straightforward reason? Why is force = mass $\times$ acceleration? I have searched in many sites but didn't actually get at it. Simply I want to know that if a mass in space moves (gains velocity thus further accelerates), how can I think, postulate and further believe that force = multiplication  of mass and its acceleration ? Is vocative comma rule vanishing? Breitbart today:   What is the source for the term nothing-burger? Propose Newbie-Overflow site or section There is no continuous injective function $f:\mathbb{R}^n\longrightarrow\mathbb{R}^m$ I have the following question, more general that   Let $U\subset\mathbb{R}^n$ be a domain. If $f:U\longrightarrow\mathbb{R}^m$  ($m&lt; n$) is a continuous function, how to prove that $f$ is not injective.  Any hint would be appreciated. Can we know the fundamental nature of space and time? Hartshorne's Algebraic Geometry defines an $\mathcal O_X$-module $\mathscr F$ to be quasi-coherent if there is an open affine cover $(U_i=\operatorname{Spec} A_i)_{i\in\mathcal I}$ of $X$ such that each $\mathscr F\rvert_{U_i}$ is isomorphic to the sheaf of modules $\widetilde{M_i}$ associated to some $A_i$-module $M_i$. It is later proved that this is equivalent to the statement that for any open affine $U=\operatorname{Spec} A\subseteq X$, there exists an $A$-module $M$ with $\mathscr F\rvert_U\cong\widetilde M$.  On the other hand, Grothendieck's Éléments de Géométrie Algébrique defines $\mathscr F$ to be quasi-coherent if every point $x\in X$ admits an open neighborhood $U\subseteq X$ such that $\mathscr F\rvert_U$ is isomorphic to the cokernel of a morphism of free $\mathcal O_U$-modules.  Now I wonder how those definitions are equal. I tried proving it by myself, but both directions seem quite nontrivial to me... Any hints? Real Analysis: Continuity of a Composition Function Suppose $f$ and $g$ are functions such that $g$ is continuous at $a$, and $f$ is continuous at $g(a)$. Show the composition $f(g(x))$ is continuous at $a$.  My idea: Can I go straight from definition and take $\delta=\min\{\delta_1,\delta_2\}$, where $\delta_1$ is used for the continuity of $g$ at $a$ and $\delta_2$ is used for f being continuous at $g(a)$. In my proof I just treat $g(a)$ as a point when referring to the composition. So it goes like this:  Proof: Given $\epsilon&gt;0$, take $\delta=\min\{\delta_1,\delta_2\}$. Then $0&lt;|x-g(a)|&lt;\delta$ which implies $|f(g(x))-f(g(a))|&lt;\epsilon$. Non-existence of $\lim \limits_{(x, y) \to (0,0)} \frac{x^3 + y^3}{x - y} $ How to show that $\lim \limits_{(x, y) \to (0,0)} f(x, y)$ does not   exist where,         $$f(x, y) =  \begin{cases} \dfrac{x^3 + y^3}{x - y} \; ; &amp; x \neq y \\  0 \; \;\;\;\;\;\;\;\;\;\;\; ; &amp; x = y  \end{cases}  $$   I tried bounding the value of the function as $(x, y)$ approaches $(0,0)$ but was not successful. I graphed the function and saw that it was actually approaching $0$ but Microsoft Math failed to render some points around the $x = y$ plane. So I imagine I need to find points $(x, y)$ such that $x$ is extremely close to $y$ but $(x, y)$ is not as close to $(0,0)$ to show that the function does not approach $0$ around the origin. But was unable to think of any.   Hints or suggestions would be awesome. Any help is appreciated. My Applications are not showing after upgrading from Ubuntu 18.04 to 20.04 I did an upgrade today to the latest version of ubuntu. Everything looked good and fine only for me to discover that I cannot find my applications after clicking the 'Show Applications' icon. The same applies when I search for an application in the search bar, I do not see it. It shows me an endless search.  These are the screenshot images of the problem:      In the meantime, I access my applications from the menu at the top bar and also use the terminal to run applications with CLI. A word for a person who always needs there to be a problem? I'm interested in Gaussian blur layer that blurring all inside of some figure located on this layer.  I mean, blurred background of some exact area. And in case of I move this area, blurred image must be updated. If I move some object in background - blur must be updated. etc. I have the following validation rule:  AND(  $Profile.Name &lt;&gt; 'System Administrator',  OR(  ISPICKVAL(PRIORVALUE(Level__c), "Archived"),  ISPICKVAL(PRIORVALUE(Level__c), "Closed")  )  )   This validation rule is on the opportunity object, and what I want to achieve is, if the picklist Level__c is either set to Archived or Closed, the opportunity record can only be edited by the System Administrator.  For some reason though, the validation rule also triggers, when I want to set the Level__c to Archived or Closed. But this is not what I want.   Any idea what's wrong with the validation rule? Why do both cron and systemd execute automatic upgrades? How to play MP3 files using Rhythmbox? If $a_0\in R$ is a unit, then  $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$ How to force the browser to reload cached CSS and JavaScript files How do I completely uninstall Google Chrome and Chromium? I'm having a problem with Chrome and one of its extensions, so I want to completely uninstall everything. I've uninstalled Chrome through the Software Center, but when I reinstall it, all of my extensions and preferences are still there.   If I want to start over from scratch, what do I need to do? How can I combine hashes in Perl? What is the best way to combine both hashes into %hash1?  I always know that %hash2 and %hash1 always have unique keys.  I would also prefer a single line of code if possible.    $hash1{'1'} = 'red'; $hash1{'2'} = 'blue'; $hash2{'3'} = 'green'; $hash2{'4'} = 'yellow';