Positive meniscus (convex-concave) lenses, with center thickness bigger, are designed to minimize spherical aberration. When used in combination with another lens, a positive meniscus lens will shorten the focal length and increase the numerical aperture (NA) of the system without introducing significant spherical aberration. When used to focus a collimated beam, as shown in the diagram above, the convex side of the lens should face the source to minimze spherical aberration.
The focal length of each lens can be calculated using the following equation:
f= (R1*R2)/((n-1)*(R2-R1)).
where n is the index of refraction and R1,R2 is the radius of curvature for each surface of the lens.
They can be also coated with MgF2 to protect the surface or AR coated to increase the transmission.