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
Lens (optics) object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length "f" are focused at a point with distance from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped