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The geometry and calculation steps to derive the transform matrix for a ray incident on a flat mirror perpendicular to the optic axis. The mirror reverses the direction of propagation while maintaining the angle of incidence and deviation from the optic axis. A diagram showing the ray's geometry and the derived transform matrix.
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α^ y^0 = y^1 0
α 0
α 1
The ray strikes the mirror and reflects at the same angle. The deviation from the optic axis is not changed by the mirror, but the direction of propagation is reversed. So we have:
y 1 = y 0
α 1 = −α 0 ( y 1 α 1
y 0 α 0
