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Light rays reflected off vertical mirror (law of reflection)

  1. Jan 21, 2015 #1
    1. The problem statement, all variables and given/known data

    1. A vertical mirror is placed at the origin. A ray of light coming from A is reflected by the mirror so that it passes through B. How far from the bottom does the ray hit the mirror? The coordinates are A = (11.4, 15.9) and B = (15.9, 4.7), in centimetres.

    2. Relevant equations
    incident angle=reflected angle
    tan@=tan@=h/x

    3. The attempt at a solution
    So, I drew my diagram, and I know that the rule of reflection means that the incident angle from A will be equal to the reflective angle to B. I'm just trying to use trig to solve it but I'm having no luck. I drew a triangle connecting A an B, with it having a hypotenuse of 12.07, solved for its other angles, and cannot seem to relate it to the mirror height.
     
  2. jcsd
  3. Jan 21, 2015 #2

    Doc Al

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    Staff: Mentor

    Here's a hint. Call point C where the light ray hits the mirror. Imagine lines (rays) from A to C and from C to B. How are those lines related?
     
  4. Jan 21, 2015 #3
    They're both arriving at/leaving C at the same angle right?
     
  5. Jan 21, 2015 #4

    Doc Al

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    Good. What other property of a line expresses the angle it makes?
     
  6. Jan 21, 2015 #5
    Can you elaborate on that a bit? I'm not really sure what you mean..
     
  7. Jan 21, 2015 #6

    Doc Al

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    Consider the slope of those lines.
     
  8. Jan 21, 2015 #7
    They would be the same I believe.
     
  9. Jan 21, 2015 #8

    Doc Al

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    Draw yourself a picture and see. How is slope defined?
     
  10. Jan 21, 2015 #9
    rise/run. the C-B slope would just be the negative of A-B's slope. I've had the picture for awhile I just can't figure out how to get the right info to solve it
     
  11. Jan 21, 2015 #10

    Doc Al

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    Exactly! You'll need to express that mathematically.

    You are given the coordinates of A and B. Set up an equation, and you can solve for the unknown height of C.
     
  12. Jan 21, 2015 #11
    so the equation i set up was:
    15.9-c/11.4= -((c-4.7)/15.9)
    This is giving me an answer that makes no sense (68.08cm)
     
  13. Jan 21, 2015 #12

    Doc Al

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    Almost. You messed up the sign.
     
  14. Jan 21, 2015 #13
    Ahhh, I see now. Thank you very much! I was trying to solve it a completely different way haha no wonder I couldn't figure it out
     
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