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Curvature to mirror and focus light?

  1. Oct 23, 2011 #1
    I posted earlier asking if my science fair idea—to use many mirrors to reflect light onto one point—would work. After getting a reply that it would, I now have another question.
    It's clear that I have to use a curved board to mount the mirrors onto, or I would just get reflection of straight light ray parallel to each other. Kinda useless. How can I find the equation for the curvature of my board? Honestly, I don't know when to start here... if it makes a difference I plan to use between 300 and 500 mirrors of 3/4 in squared to an 1inch squared area each.
    All help appreciated!
     
  2. jcsd
  3. Oct 23, 2011 #2
    How small of a point do you want to make? Obviously a 1" flat mirror will only make a 1" spot, so that would be the diameter of your focal spot - to do better you need more smaller mirrors.

    Radius of board = distance from the board to the focal spot.
     
  4. Oct 23, 2011 #3
    Well, I don't honestly have to heat that much, I'm heating water so I only need 100 degrees celsius.
    At any rate, I was thinking 1" squared of about 500 mirrors. I suppose I could use smaller mirrors but the smallest I found online are 3/4 inch squared. What I'm looking for is the cross sectional curvature.
     
  5. Oct 23, 2011 #4
    It doesn't matter if the mirrors are flat (which is what I assumed you were doing) or curved, the only radius that matters is the distance from the mirror to the focal point. If you want to focus light to a 1" spot with a bunch of flat 1" mirrors, you mount them on a board a distance R away from the spot and bend the board to a radius R. If you use a bunch of spherical mirrors with radii R instead, you still get a spot but it's a smaller spot.
     
  6. Oct 23, 2011 #5
    I meant the curvature of the board, like you said, I'm using straight mirrors.
    So what you're saying is that my board has to be an arc segment of a circle, essentially?
     
  7. Oct 23, 2011 #6

    jtbell

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    No, the focal length is half the radius of curvature.

    http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/mireq.html

    Beware that this works for a spherical mirror only if the size is not too large compared to the radius of curvature. When the mirror gets beyond a certain size (for a fixed radius), you get spherical aberration and incoming parallel rays don't converge to a single point.

    http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/aber.html

    (This illustrates it for a lens with spherical surfaces, but the same thing happens with mirrors.)

    A parabolic shape would be better, in principle. Maybe it won't make much difference because you're using flat mirror segments so you're going to get a fairly crude focus anyway.
     
    Last edited: Oct 23, 2011
  8. Oct 23, 2011 #7
    Hmm...I think I could probably find the radius of curvature with differentiation...so essentially any parabolic shape would work? A different parabolic equation would only change the location of the focal point?
    Do you think I could hit boiling temperatures with this?
     
  9. Oct 23, 2011 #8
    Yes, there is a 2 in there, forgot about that.
     
  10. Oct 23, 2011 #9
    For your purposes you don't need to worry about a parabola vs. a sphere.
     
  11. Oct 23, 2011 #10
    Actually, parabola is probably easier for me to get ahold of in my area, I'm just wondering if a parabola will hit the minimum of 100 degrees celsius.
     
  12. Oct 23, 2011 #11

    DaveC426913

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    Thundagere

    1] You don't need to curve the panel upon which the mirrors sit. Mount them on a flat board and simply angle each mirror. This will be way easier to construct.

    2] To ensure the mirrors are focusing properly throw away your pencil and paper - do it for reals. Just shine a light on the mirror and simply adjust the mirror until its spot of light is centred on your focus.
     
  13. Oct 23, 2011 #12
    How would I angle it....as in, how would I get it, practically, to stick in that position?
     
  14. Oct 23, 2011 #13

    DaveC426913

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    How permanent do you want it? A big wad of plastercine would do it.

    But permanently, what you do is attach one side to the base and the other side is held in place with a nut and bolt system that can be adjusted and fine tuned. Dial the bolt up to deflect the mirror one way, dial it down to deflect it back. Or even simpler, two mirror edges held in place with screws and one or more shims placed underneath. Tighten the screw against the shim.

    The exact mechanism would be left up to you. It would be dependent on the materials you have available, the amount of angle and the size of the mirror. I could draw you a diagram of a proposed idea, but it would mostly be experimenting.

    You'll need some system like this anyway, since with your method, if it is fixed in place, you would have no way of fine-tuning the mirrors. And you'll need to, I assure you.
     
  15. Oct 23, 2011 #14
    Yeah, I think I'll probably use the shim method. It'll take longer, but it solves the problem of mirrors drooping down over time.
    The only thing is, I'll hae to drill through the mirror for that and place the bolt+shim. Would that overly interfere with the light focusing? I think I'll still reached desired temperatures, but since I have no frame of reference...
     
  16. Oct 23, 2011 #15

    DaveC426913

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    No need to put any holes in the mirrors. Hold them by their edges.
     
    Last edited: Oct 23, 2011
  17. Oct 23, 2011 #16
    Ah, I'm not quite sure what you mean...could you elaborate?
    Sorry, I'm in middle school. Studied theoretical physics, but... I don't have much practical experience.
     
  18. Oct 23, 2011 #17
    I hope you've considered the time and effort required to fine-align 500 mirrors. :eek:
     
  19. Oct 23, 2011 #18
    Don't worry. I have at least 6 months. Maybe a bit more ;).
     
  20. Oct 23, 2011 #19

    DaveC426913

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    See diagram attached.

    One edge of the mirror rests on a fulcrum so it can tilt.
    Two other edges have washers glued to the back of the mirror.
    Screws or bolts run through washers. Use double nuts to clamp washer.
    Adjust mirror by dialing nuts up or down.

    The reason you need so many nuts is because
    1] every nut must be a pair, so they lock in place
    2] You need 2 nut pairs for each screw, top and bottom
    3] You need two screws for two axes.
    A total of 8 nuts per mirror.
     

    Attached Files:

    Last edited: Oct 23, 2011
  21. Oct 23, 2011 #20

    DaveC426913

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    Tru dat!
     
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