Thin lens is the index of refraction of the lens material, and "R" and "R" are the radii of curvature of the two surfaces. For a thin lens, "d" is much smaller than one of the radii of curvature (either "R" or "R"). In these conditions, the last term of the Lensmaker's equation becomes negligible, and the focal length of a thin lens in air can be approximated by Here "R" is taken to be positive if the first surface is convex, and negative if the surface is concave. The signs are reversed for the back surface of the lens: "R" is
Compound refractive lens the order of meters, by using many lenses in series. To minimize the absorption the lens must be made from a material such as aluminium, beryllium, or lithium. CRLs were first demonstrated in the mid-1990s by a group of scientists at the ESRF. They drilled holes in an aluminium block, and achieved focusing in two dimensions. For X-rays a concave lens focuses the X-rays because the index of refraction is slightly below unity. In a CRL of this type the walls between the cylindrical holes act as concave lenses for X-rays traveling perpendicular to the axis of the drilled cylinders.