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I Geometrical Optics - Light ray angles on a spherical mirror

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  1. Nov 20, 2018 #1
    upload_2018-11-20_20-41-22.png
    I can't see how the textbook produces the following relationships between angles:
    $$ \theta = \phi + \alpha \qquad (1)$$
    $$ 2\theta = \alpha + \alpha ' \qquad (2)$$

    My thinking is that the exterior angle theorem for triangles was used to create expression ##(1)##, but I am unsure as to how expression ##(2)## came about. Was the exterior angle theorem simply used twice to produce both equations?
     
  2. jcsd
  3. Nov 20, 2018 #2

    DaveC426913

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    Gold Member

    (2) comes about by the exact same theorem as (1).

    2θ,α,α′ is the identical setup as θ,α,ϕ - it just makes a stubbier triangle.

    angles.png
     
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