# 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)

This is in contrast to the definition of concave lens, which does seem to remain valid:

(Attribution: DrBob at the English language 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:

1. Is the author's definition valid?
2. Is my definition valid?
3. What is the general definition of a "convex lens"?

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

• The percise definition of convex lens is not so importent. The important thing is to understend where the light goes when it hits the lens. Commented Jan 8, 2020 at 22:01
• @AdiRo Hmm, do you mean that the positive/negative lens distinction is more important than the convex/concave distinction? Commented Jan 8, 2020 at 22:02
• No... I mean that you can think of many lens - positive negative, spherical, or anything else. You can call them what you want, as long as you understand how light changes it's angle when it hits them Commented Jan 8, 2020 at 22:08
• Your definition is equivalent to his. 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: What makes you say this? Everything here seems perfectly consistent to me.
– user4552
Commented Jan 8, 2020 at 22:33
• I suspect there is some misinterpretation going on wrt what "centre/edge of the lens" refers to. If you clarify what you mean by "it doesn't even have a centre thickness" (from your comment on the second Wikipedia image) I think the misunderstanding will be quick and easy to resolve. Commented Jan 9, 2020 at 0:44

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.

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.

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.