How can you tell if a surface is convex or concave before drawing it?

[channel1]

Homework Statement

How do you tell if a spherical refracting surface is convex or concave before drawing a ray diagram? (given the indices of refraction, center of curvature, s, and s')

Homework Equations

i read this:
"A convex surface is one that bulges out in the middle toward the object, so that its center of curvature is on the opposite side of the surface from the object. Therefore a surface is convex if R and s have opposite signs."
http://www.physnet.org/modules/pdf_modules/m222.pdf

The Attempt at a Solution

but according to my diagrams from class, an object for either convex or concave surfaces can be inside the surface so the above quote can't be true...

 

[jbsteele]

If R and s have the same signs, then the surface is concave. If R and s have opposite signs, then the surface is convex.