# I Geometrical Optics - Light ray angles on a spherical mirror

Tags:
1. Nov 20, 2018

### I_laff

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. Nov 20, 2018

### DaveC426913

(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.