Definition of a convex lens? I am currently studying the textbook Modern Optical Engineering, fourth edition, by Warren Smith.
Smith defines convex lenses as follows:

Figure 1.8 diagrams the action of a convex lens -- that is, a lens which is thicker at its centre than at its edges.


He then defines concave lenses as follows:

In Fig. 1.9 the action of a concave lens is sketched. In this case the lens is thicker at the edge and thus retards the wave front more at the edge than at the centre and increases the divergence.


Smith's definition of a convex lens is obviously not at all rigorous, but, when using figure 1.8 as a reference, one can see that the edges of the lens do indeed seem to clearly be thicker than the centre region of the lens. However, if one looks at other commonly used images of lenses, such as those from the Wikipedia article for lens, it is not at all clear that this definition is valid:

(Attribution: DrBob at the English language Wikipedia)

(Attribution: Fir0002 on en.wikipedia)
This is in contrast to the definition of concave lens, which does seem to remain valid:

(Attribution: DrBob at the English language Wikipedia)

(Attribution: Fir0002 on en.wikipedia)
It seems to me that these lenses should be defined in terms of their radius of curvature: If $R_1$ is the radius of the first edge, and $R_2$ is the radius of the second edge, then convex lenses are lenses with radius of curvature $R_1 = -R_2$, where $R_2 > 0$, and concave lenses are lenses with radius of curvature $R_2 = -R_1$, where $R_1 < 0$.
So my questions are as follows:

*

*Is the author's definition valid?

*Is my definition valid?

*What is the general definition of a "convex lens"?

I would greatly appreciate it if people would please take the time to clarify this.
 A: A good definition for me is: if the surfaces of each side are sections of a sphere and the thickness of the centre is smaller than the edges its a divergent lens. If it is bigger, it is a convergent lens. The radius can also be infinite in one of the sides, that means one of them can be plane. 
A: The degree of varying thickness in the lens is not a rigorous method of knowing what type of lens you have. It may work if it is a biconcave or biconvex lens but not for the others. If you have a lens at hand and want to find its nature, try finding its focal point. If the focal point is positive (converges light), it is a convex lens and if it is negative (diverges light), it is a concave lens.
A: My apologies everyone; I was misunderstanding the terminology. 
https://www.newport.com/medias/sys_master/images/images/h6d/hde/8933922275358/BI-CONVE-XLE-S.pdf
https://www.newport.com/f/ar14-n-bk7-bi-convex-lenses
The spec. sheets for the biconvex lenses describe "Center Thickness" as $T_c$. This is in accordance with what the textbook author describes, as well as $d$ in the Wikipedia article.
Thank you to the people who took the time to post comments.
