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1. Don't forget about the normal for refraction. It may be more intuitive to think about angles of incidence and reflection relative to the object surface, but that kind of thinking will lead to some serious midterm heartache. Just remember that in all of these diagrams there is always a normal and what's the point in drawing the line if we're not going to use it?
2. It's all too easy to memorize what different mirrors and lenses do and then get things all mixed up because convex mirrors do the exact opposite of lenses:
We don't mean to beat a dead horse but it'seasy to get mixed up. Use the ray diagrams. The ray diagrams for a convex mirror and a convex lens are similar, etc.
3. Watch out for the sign conventions when using the mirror and especially the thin lens equation. We can get really strange numbers if we don't use the right sign using the lens equation. Remember, virtual images have negative image distances! And any image, real or virtual, that's upside down has a negative image height. Double check the numbers from the equations by sketching a ray diagram: they should match.