Patent ID: 8016460

Claim:
A converging element for a light-emitting diode (LED), adapted to converge a light ray emitted from a light-emitting chip to enable the light ray to form an approximately parallel light ray after passing through the converging element for an LED, comprising: a cylinder, disposed on the light-emitting chip, wherein a height and a radius of the cylinder satisfy Equation 1: tan - 1 ⁡ ( a h ) - tan - 1 ⁡ ( a h - d 2 ⁢ ⁢ h ) ≤ 1 ⁢ ° , Equation ⁢ ⁢ 1 wherein h is the height of the cylinder, a is the radius of the cylinder, and d is a side length of the light-emitting chip; and a first lens, disposed on the other end of the cylinder opposite to the light-emitting chip, wherein the first lens has a first plane and a first curved surface opposite to each other, the first plane of the first lens is attached to the cylinder, and the first curved surface of the first lens satisfies Equation 2: tan ⁢ ⁢ θ = ⁢ tan ⁡ ( β 2 - β 1 ) = ⁢ tan ⁢ ⁢ β 2 - tan ⁢ ⁢ β 1 1 + tan ⁢ ⁢ β 2 ⁢ tan ⁢ ⁢ β 1 = ⁢ a h , ⁢ ⁢ tan ⁢ ⁢ β 1 = ⁢ sin ⁢ ⁢ β 1 cos ⁢ ⁢ β 1 = ⁢ n 2 n 1 ⁢ sin ⁢ ⁢ β 2 1 - ( n 2 n 1 ⁢ sin ⁢ ⁢ β 2 ) 2 = ⁢ n 2 n 1 ⁢ 2 ⁢ ⁢ Δ ⁢ ⁢ h a 2 + ( 2 ⁢ ⁢ Δ ⁢ ⁢ h ) 2 1 - ( n 2 n 1 ⁢ 2 ⁢ ⁢ Δ ⁢ ⁢ h a 2 + ( 2 ⁢ ⁢ Δ ⁢ ⁢ h ) 2 ) 2 , ⁢ ⁢ and ⁢ ⁢ tan ⁢ ⁢ β 2 = 2 ⁢ ⁢ Δ ⁢ ⁢ h a ; Equation ⁢ ⁢ 2 wherein n 1 is a refractive index of the cylinder and the first lens, n 2 is a refractive index of air, and Δh is a minimum distance between a center point of the first plane of the first lens and a center point of the first curved surface of the first lens.