I thought that hole smaller than wavelength causes strong diffraction.    Holes in door of the microwave oven 100 times smaller than wavelength. Why does it block radiation?
This is a follow-up to this question:   Hans Bethe wrote a paper in 1944, "Theory of Diffraction by Small Holes," Phys. Rev. 66, 163. I don't have access to the paper, but from descriptions online it sounds like he proved the following. Suppose a plane wave impinges on an absorbing sheet, and there is a hole in the sheet of diameter $d$, with $d&lt;\lambda$. Let $P_0$ be the power incident on the hole, and $P$ the power diffracted through the hole. Then the transmission is $T=P/P_0=(d/\lambda)^4$.  As a practical application, I think this explains why microwaves don't leak strongly through the metal grille in the front of a microwave oven.  Questions:   Does the thickness of the sheet matter? From references online, it sounds like the hole is treated as a waveguide...? This seems to relate to cutoff frequencies of waveguides, etc.? It seems to me that Huygens' principle would give $T=1$ for $d\ll\lambda$, since in this limit the wavelets are in phase. Why is Huygens' principle invalid here? Is this related to question #1? Is there a simple argument for the proportionality to $(d/\lambda)^4$? Or if not, how does one prove this using the gory details of Bessel functions, etc.?
How do I view 'git diff' output with my preferred diff tool/ viewer? When I type git diff, I want to view the output with my visual diff tool of choice (SourceGear "diffmerge" on Windows). How do I configure git to do this? How should a user's death be handled? $_POST empty on utf-8 characters Redirect all requests to HTTPS, except for one subdirectory Did the law of conservation of energy apply to the earliest moments of the Big Bang? If so, what theoretical physics supports this?   I hear that Einstein's theory of relativity disputes the law of conservation of energy- so does that mean the law is false, or only some aspect of it? Package babel Error: Unknown option `francais' In the comment field on StackOverflow (and other StackExchange sites as well, I presume) you're required to write 15 characters for the server to accept your post. If a shorter post is submitted, an information message states that the comment is too short. That is all good.  However, below the comment field is a counter, which counts up to 15 and then down from however many characters you're allowed to type minus fifteen. This counter doesn't always act the same as the actual validation: if I pad my message with whitespace, the validation notices and still says the message is too short, but the counter does not notice, and counts as usual.  Suggested fix: make the character counter trim the message before it counts, so the two messages say the same thing. Modify systemd unit file without altering upstream unit file I have installed the pimd service by means of apt. This comes with an upstream systemd unit file (/lib/systemd/system/pimd.service).  I want the service to be restarted when for some reason it gets killed, hence I wish to add the line Restart = always in the unit file.   However, I don’t want to modify the upstream unit file.  Is there any workaround for this? What is the difference between:   The company would rather each employee be provided with ID card.  The company would rather each employee were provided with ID card. How to open a particular port in ubuntu? My SoulSeek client Nicotine+ checks my open ports during initial configuration and promts that the one port number it needs is closed, cutting me off frmo about 50% of the users. Is there anyway I can open that particular port for the application to use?  RUnning ubuntu desktop 13.04. I have not manually installed any firewalls, but not sure if its included in the default installation. Sql Server Indexes Include Primary Key? How to test real network throughput between two points? What are some of the better tools/utilities for testing real bandwidth across a link?  In my case I am testing the real throughput across a wifi bridge. What is the probability that a shuffled standard deck of 52 cards has no two cards of the same rank together ?  I am unable to get a handle on this problem, and wonder whether there is an analytical solution ? How can I read inputs as numbers? Can Ubuntu use all my 4GB of RAM? How to deal with hierarchical / nested data in machine learning Making a div vertically scrollable using CSS I was amused by the expression "Paid a penny and only farted" (related by @FumbleFingers), which suggested a similar Japanese saying: 大山鳴動鼠一匹 - "Find only a small mouse coming out after hearing rumblings and experiencing shaking of the big mountain."  It’s humorous. I chuckled when I read it, and I wrote to the author that I love it.  With that said, the word "fart" reminds me of another Japanese proverb, 百日の説法屁一つ- "A fart ruins 100 days of sermons by the priest", which means that a small mistake (the sound of a fart in front of the congregation) brings all his efforts to naught.  It can’t happen in big Western churches. But it could well happen in a small wooden temple where a priest would preach to 30 – 50 provincial followers. Can you imagine how the proud priest being called 'the venerable' would be embarrased when his loud fart is heard by all his followers during his serious sermon and they start to giggle here and there in the hall?  We also have a similar saying" 九仞の功を一簣に欠く, which literally means "Collapse a 9- meter sand tower with the last pile of sand."  What is the English equivalent of the saying "A fart ruins 100 days of sermons by the priest (bishop): a small mistake depreciates the value of (vitiates) all labor and effort to naught," preferably in such a humorous way? How does Wild Shape work with special ways to calculate your AC? Among the effects of Wild Shapes, these two:     Your game Statistics are replaced by the Statistics of the beast, but   you retain your alignment, personality, and Intelligence, Wisdom, and   Charisma scores. You also retain all of your skill and saving throw   proficiencies, in addition to gaining those of the creature. If the   creature has the same proficiency as you and the bonus in its stat   block is higher than yours, use the creature's bonus instead of yours.   If the creature has any legendary or lair actions, you can't use them.      You retain the benefit of any features from your class, race, or other   source and can use them if the new form is physically capable of doing   so. However, you can't use any of your Special senses, such as   Darkvision, unless your new form also has that sense (PHB p.67, "Wild Shape")   Seem to come into conflict with each other when things like Draconic Resilience:     When you aren't wearing armor, your AC equals 13 + your Dexterity   modifier. (PHB p.102, "Draconic Bloodline")   and Barbarians:     While you are not wearing any armor, your Armor Class equals 10 + your Dexterity modifier + your Constitution modifier. You can use a Shield and still gain this benefit.   and Monks:     Beginning at 1st level, while you are wearing no armor and not wielding a Shield, your AC equals 10 + your Dexterity modifier + your Wisdom modifier.   and Stone Sorcerers:     As an action, you can gain a base AC of 13 + your Constitution   modifier if you aren’t wearing armor, and your skin assumes a stony   appearance. This effect lasts until you end it as a bonus action, you   are incapacitated, or you don armor other than a shield.   How would these resolve? [Probability]need help to understand the following expression So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively.  assume c is a constant.  I am having huge trouble to understand the integration of the following expression.  $P(Y&lt;c/u(X))$  $=\int_{t}^{\infty}f_X(x)\int_{0}^{c/u(x)}f_Y(y)dydx +\int_{0}^{t}f_X(x)\int_{c/u(x)}^{\infty}f_Y(y)dydx$  where t is the cross-point that $u(x)$ change sign    here $c/u(x)$ is given by the plot below, t is the point crossing the zero:   Confusion:   I don't understand the second integration of the second term "$\int_{c/u(x)}^{\infty}f_Y(y)dydx$", this isn't right because Y an X only defined for y>0, and x>0. So it's the first quadrant in this plot.