The sides of a spoon as concave/convex mirrors

Question

I recently saw a lecture that said the following regarding the sides of a spoon as concave/convex mirrors:

1. The concave inside of the spoon must be a positive focal length mirror because it would take normally incident rays and bend them towards the axis.

2. Conversely, the convex outside of the spoon must be a negative focal length mirror because it bends rays away from the axis.

I immediately found this perplexing, since my understanding is that it precisely is the opposite. Wikipedia (seemingly) agrees with me and says the following:

If the lens is biconvex or plano-convex, a collimated beam of light passing through the lens converges to a spot (a focus) behind the lens. In this case, the lens is called a positive or converging lens. For a thin lens in air, the distance from the lens to the spot is the focal length of the lens, which is commonly represented by $f$ in diagrams and equations.

If the lens is biconcave or plano-concave, a collimated beam of light passing through the lens is diverged (spread); the lens is thus called a negative or diverging lens. The beam, after passing through the lens, appears to emanate from a particular point on the axis in front of the lens. For a thin lens in air, the distance from this point to the lens is the focal length, though it is negative with respect to the focal length of a converging lens.

Am I misunderstanding or misinterpreting something here?

I would greatly appreciate it if people could please take the time to clarify this.

Answer 1

Your first quote deals with a mirror lens, reflection, the second quote refers to light passing through a clear lens, refraction.