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How do you derive the mirror equation with a convex mirror?

  1. May 29, 2017 #1
    1. The problem statement, all variables and given/known data
    Derive the mirror equation for a convex mirror (Si*So=f^2). Do not use a Ray heading toward the center of curvature point (C).
    Si - distance between the object's image and the focal point.
    So- distance between the object and the focal point.
    Do- distance between the mirror and object.
    Di- distance between the mirror and the object's image.
    f- focal length
    2. Relevant equations
    1/do + 1/di = 1/f

    3. The attempt at a solution
    My work is all on the picture. I am trying to get to the equation SoSi=f^2 but I don't get the right equation so I am wondering if I made a mistake in my diagram?
     

    Attached Files:

  2. jcsd
  3. May 30, 2017 #2

    haruspex

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    Look at the ray you have starting horizontally. Where it hits the mirror, draw the normal to the mirror at that point. What should be the relationship between that incident ray, the normal, and the reflected ray?
     
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