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File: AMirrorCopied ''' <link rel="alternate" type="application/rss+xml" ''' href="/rss.xml" title="RSS Feed"> ********> width="25%" |>> ''' <a title="Subscribe to my feed" ''' rel="alternate" ''' href="https://www.solipsys.co.uk/rss.xml"> ''' <img style="border-width: 0px;" ''' src="https://www.feedburner.com/fb/images/pub/feed-icon32x32.png" ''' align="middle" ''' alt="" />Subscribe!</a> _ ''' <a href="https://twitter.com/ColinTheMathmo"> ''' <img src="https://www.solipsys.co.uk/new/images/TwitterButton.png" ''' title="By: TwitterButtons.net" ''' width="212" height="69" ''' alt="@ColinTheMathmo" ''' /></a> <<| ---- My latest posts can be found here: * ColinsBlog ---- Previous blog posts: * TheOtherOtherRopeAroundTheEarth * PhotocopyAMirror * ThePointOfTheBanachTarskiTheorem * SieveOfEratosthenesInPython * FastPerrinTest * RussianPeasantMultiplication * FindingPerrinPseudoPrimes_Part2 * FindingPerrinPseudoPrimes_Part1 * TheUnwiseUpdate * MilesPerGallon * TrackingAnItemOnHackerNews * HackerNewsUserAges * PokingTheDustyCorners * ThereIsNoTimeForThis * PublicallySharingLinks * LearningTimesTables * GracefulDegradation * DiagrammingMathsTopics * OnTheRack * SquareRootByLongDivision * BeyondTheBoundary * FillInTheGaps * SoftwareChecklist * NASASpaceCrews * TheBirthdayParadox * TheTrapeziumConundrum * RevisitingTheAnt * TheAntAndTheRubberBand * IrrationalsExist * MultipleChoiceProbabilityPuzzle * RandomEratosthenes * WrappingUpSquareDissection * DissectingASquarePart2 * DissectingACircle * DissectingASquare * AnOddityInTennis * DecisionTreeForTennis * DecisionTreesInGames * AMatterOfConvention * DoYouNourishOrTarnish * BinarySearchReconsidered * TwoEqualsFour * TheLostPropertyOffice * TheForgivingUserInterface * SettingUpRSS * WithdrawingFromHackerNews ---- Additionally, some earlier writings: * RandomWritings. * ColinsBlog2010 * ColinsBlog2009 * ColinsBlog2008 * ColinsBlog2007 * ColinsBlogBefore2007 ******** !!! A Mirror Copied - 2015/08/16 [[[> This page has been _ TaggedAsPuzzles ]]] So earlier I asked: What do you get when you photocopyamirror? But the real question, as I then expanded, is not "What do you get?" but: "Why *must* you get that?" Can we deduce from first principles, based only on what a good photocopier must do, what the result will be? I claim the answer is "Yes," although there are some who disagree. Let me explain. Consider two physical instances of a brochure. They are identical, except that one is printed on matt paper, the other on glossy. We would want a photocopier to produce the same result in each case. We would not want the glossy version to have extra, spurious ghost images of any kind. So that means that the glossy surface must not send any extra light back into the receiver. The only light bounced back into the receiver must be from the brochure itself, and not from the surface. So we can consider two collections of photons: those that bounce off the brochure content, and those that bounce off the glossy surface. [[[>50 The glossy reflections are "specular", and the reflections from the non-glossy parts is "diffuse reflection." What we're arguing here is that a photocopier must be set up to copy the diffuse reflection and not the specular reflection. ]]] So the photons from the glossy surface must not affect the final result - it must be as if they didn't exist. So any glossy surface must not result in photons going to the receiver. But a mirror is the ultimate glossy surface. That means that when we photocopy a mirror there must be no photons received by the copier. |>> ********> width="20%" ******** width="20%" A mirror must send no photons to the receiver. ******** width="10%" ******** width="20%" A totally black object sends no photons to the receiver. ******** width="20%" ********< <<| So we deduce that a mirror must look to the photocopier the same as a totally black object. Thus photocopying a mirror must result in a completely black image. Are you convinced? ''' <a href="mailto:PhotocopyAMirror@solipsys.co.uk">Send us email</a> and tell us what you think. ---- |>> | |>> <<<< Prev <<<< ---- TheOtherOtherRopeAroundTheEarth <<| | : | |>> >>>> Next >>>> ---- TheMutilatedChessboardRevisited ... <<| | ---- ********> ''' <a href="https://twitter.com/ColinTheMathmo">You should follow me on twitter</a> ******** ''' <a href="https://twitter.com/ColinTheMathmo"> ''' <img src="https://www.solipsys.co.uk/new/images/TwitterButton.png" ''' title="By: TwitterButtons.net" ''' width="212" height="69" ''' alt="@ColinTheMathmo" ''' /></a> ********< <<| ---- !! Comments I've decided no longer to include comments directly via the Disqus (or any other) system. Instead, I'd be more than delighted to get emails from people who wish to make comments or engage in discussion. Comments will then be integrated into the page as and when they are appropriate. If the number of emails/comments gets too large to handle then I might return to a semi-automated system. That's looking increasingly unlikely. ********<