Light can be concentrated by lenses by placing either a biconvex or plano-convex lens (see figure 1) in the path of light rays traveling parallel to the lens axis (located in the middle of the lens, and along the horizontal dotted line in figure 1).
where n is the index of refraction of the lens; R1 is the radius of curvature facing the oncoming rays; R2 is the radius of curvature for the lens surface on the outgoing rays side; and d is the lens thickness measured at the center of the lens. R1 and R2 can be found by tracing over a curved surface of the lens and continuing this curve to form a circle, then finding the radius of that circle.
Simple lenses all suffer from chromatic aberration; this is where the lens glass has a higher index of refraction for blue light than for red light (Gibilisco 2009). The focal length of the red light is then longer than the focal length for the blue light, since the glass bends blue light more. This effect causes refracting telescopes and cameras that use convex lenses to have blurry images; this effect can also make stars appear to have rainbow halos. Multiple layers of glass with different indices of refraction can be laminated to form a compound lens, which corrects for this chromatic aberration.
Light can also be concentrated by mirrors. Parallel light rays will hit a concave mirror (see figure 3), reflect back and focus at the focal point (on the same side of the mirror as the oncoming rays). Reflecting telescopes use this configuration to focus distant starlight, but usually have a secondary mirror placed before the focal point to reflect the focused light into a different plane (such as up through the telescope top in a Newtonian telescope) for viewing.
We can also calculate the focal length of the concave mirror if the distance from the center of the mirror to an object is known ( = r0), and the distance from the center of the mirror to the