Some embodiments provide a light-emitting device comprising: a light-emitting diode; a substantially transparent encapsulating material having a refractive index in the range of about 1.3 to about 1.8; a layer of low refractive index material having a refractive index in the range of about 1 to about 1.2; and a translucent ceramic phosphor having a refractive index in the range of about 1.6 to about 2.7, and is substantially dome-shaped with substantially uniform thickness. Some embodiments provide a light-emitting device comprising: a substrate; a light-emitting diode mounted on a surface of the substrate; and a substantially hemispheric cover mounted on the surface of the substrate so as to enclose the light emitting diode; wherein the substantially hemispheric cover comprises an outer layer, a middle layer, and an inner layer arranged concentrically, with the inner layer being nearest the light-emitting diode.