An optical element (100), for a lamp or lighting apparatus having one light-emitting diode (LED) as a light source, that distributes unidirectional light output from the LED into an omnidirectional output with a controlled variance in light intensity, is provided. A diffuser can also be used around the optical element and the LED to provide further distribution of the light rays by e.g. scattering. The optical element (100) is positioned adjacent to the LED and defines a central axis (CA) and a lateral axis (L) that is substantially orthogonal to the central axis (CA). The optical element (100) extends circumferentially about the central axis (CA) and comprises a convex light-receiving surface (102) that is symmetrical about the central axis (CA) and positioned adjacent to the LED; a frusto-conical light-projecting surface (104) positioned laterally outside the convex light-receiving surface (102) and substantially symmetrical about the central axis (CA); and an curved light-reflecting surface (114) positioned laterally inside the frusto-conical light- projecting surface (104) and substantially symmetrical about the central axis (CA). The curved light-reflecting surface (114) is spaced apart along the central axis (CA) from the convex light- receiving surface (102).