Light emitting device having a specific dimension of phosphor layer

A light emitting device, comprising:

• a base;
• a light emitting diode (LED) supported by the base;
• a first layer spaced apart from the LED and comprising a light emitting material, the first layer having a refractive index n1, wherein an enclosure formed by the first layer and the base encloses the LED, and wherein a medium inside the enclosure between the LED and the first layer has a refractive index n0 that is less than n1;
• and
• an optic element in contact with the first layer and having a refractive index n2 that is at least equal to n1, the first layer being positioned between the optic element and the LED,
• wherein the optic element has, at a surface of contact with the first layer, a radius r measured along a ray originating from the LED, and, at an output surface of the optic element, another radius R measured along the same ray originating from the LED, such that R is at least equal to r·(n2/nm),
• wherein nm is the refractive index of a medium adjacent the output surface of the optic element,
• wherein a dimension of the first layer corresponds to the radius r,
• wherein the radius r is at least equal to √[A/(4πP)],
• wherein A is the surface area of the LED, and
• wherein P is a specified fraction of reentry.