Optical efficiency of LEDs with hemispherical lenses.

In this paper formulas are derived that describe the optical efficiency of an LED package consisting of a hemispherical lens placed on the cylinder. The dependence of this efficiency on the H/R ratio and the epoxy coefficient of refraction is calculated. In calculations it is assumed that the semiconductor chip, believed to be the point source of radiation, is mounted on the optical axis of the LED package, and the absorption of nonscattering epoxy is small. As an example, the optical efficiency of the LED with H/R = 2.5 and n = 1.5 is calculated: it is equal to 37.4%.