How does this mirror NOT flip its image?

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As mentioned in the comments, Dr. Hicks published a brief explanation of the mathematical construction he uses in Physics Today ["The customized reflections of freeform mirrors," Phys. Today, Oct. 2010, p. 72]. Here's a link for those who have access. Beware, however, that his idea of image formation by mirrors in incorrect - he indicates that the image in a plane mirror can lie in front of the mirror, in the same plane as the object, for instance. But the gist is this: Imagine observing the mirror image through a fixed pinhole, representing the pupil of a camera or the observer's eye. A light ray that emanates from a point q on the object (the person's right hand, say) bounces off the mirror and then goes through the pinhole, but it must approach the pinhole from a point p in the same plane as the object, but on the left. That tells you where to place a small segment of the mirror, and at what angle - it has to lie along the vector from the pinhole through p, and depending on its distance in the x direction (away from the pinhole), it has to be at an angle to deflect a ray from q through p and through the pinhole. If you can construct a continuous surface that does that for every point q on the object, you've got your "reversing" mirror. The solution is not unique, and he says it can only be done approximately. He doesn't give the details of his solution, but says it's "saddle shaped," and works within 3 cm of the optical axis, for objects 34 ± 1 cm from the mirror.

Note that ordinary plane mirrors do NOT reverse the image. The reason text appears reversed in the mirror is because you turn the text around to present it to the mirror. (If the text were on a transparency, you would see the text the same way both on the object and on its image in the mirror.) So this device actually DOES flip its image, which is what makes it special. Note also that a mirror that is a concave parabola horizontally should work similarly for objects farther than its focal length, though it won't in general preserve the size of the image, except if the image is at the right distance from the mirror. (But then, I suspect Dr. Hicks' probably wouldn't either...)

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Updated on October 14, 2020

Comments

  • user541686
    user541686 about 3 years

    Years ago, Professor Andrew Hicks invented a mirror that doesn't flip its image.

    I know it was done via computer modeling to make light traverse specific paths, but that sounds basically like black magic -- I don't understand how it works from an optics standpoint.

    Can someone please explain how it actually works, hopefully with a diagram?

    • lemon
      lemon about 7 years
      It's presumably just a concave mirror, curved such that the right hand is reflected back from the left side, etc...
    • HolgerFiedler
      HolgerFiedler about 7 years
      @MasterOfMuppets Seems your link doesn't work properly, try this en.m.wikipedia.org/wiki/Non-reversing_mirror
    • Communisty
      Communisty about 7 years
      @lemon this wikipedia page disagrees: Non-reversing_mirror . It only has a short explanation of the invention and quite frankly I would also like to hear a deeper explanation. And the article the question asker posted doesn't tell if the mirror has only one focal point where the mirror image is created accurately like in a concave mirror or does it work in any distance, but I guess it wouldn't have been an amazing invention if it only does what the concave mirror does with numerous mini-mirrors.
    • Farcher
      Farcher about 7 years
      There is an article in Physics Today but alas I cannot access it. scitation.aip.org/content/aip/magazine/physicstoday/article/‌​63/…
    • OON
      OON about 7 years
      I think it's interesting to look at this photo of that mirror at angle roomeast.com/wordpress/wp-content/uploads/2012/08/…
    • Admin
      Admin about 7 years
      A mirror flips left right but does not flip up down. So if you want no left right flip, you just need to rotate pi/2. (sorry for the stupid joke)
    • Stéphane Rollandin
      Stéphane Rollandin about 7 years
      Another related article: laserfocusworld.com/articles/2012/07/… (by Hicks himself)
  • user541686
    user541686 about 7 years
    I really appreciate the answer but the main thing I haven't understood (and still don't) is how it can work when the viewing spot (pinhole here) isn't at a fixed position relative to the mirror. It intuitively seems impossible to me, but it seems(?) he has done it somehow. Do you understand that aspect of it?
  • user541686
    user541686 about 7 years
    (I wasn't the downvoter by the way.)
  • pwf
    pwf about 7 years
    I suspect it only works for viewing locations near the axis, since he only claims his solution works for a mirror "surface confined to the rectangular volume x = 34 ± 1 cm, y = z = 0 ± 3 cm". That's a fairly small range of viewing angles (± 5º).