# Can a biconcave thick lens ever have a positive focus? I.e. if both sides have radius of curvature -/+R?

Since a thin biconcave lens has a negative focus, can a thick biconcave lens with a certain thickness have a positive focus if both sides have the same (magnitude) radius of curvature?

Gullstrand's equation says that the equivalent power of a thick lens ($P = 1/f$) is given in terms of its front and rear surface powers $P_1$ and $P_2$ by $$P = P_1 + P_2 - P_1 P_2 \frac{d}{n},$$ where $d$ is the separation between the surfaces and $n$ is the index of refraction of the lens material. For concave surfaces, $P_1$ and $P_2$ are negative, and $d$ and $n$ are always positive. Thus, the equivalent power will always be negative, which means that the equivalent focal length would always be negative as well.