Some of the first LED's I bought were shaped like a small cupcake with a gold ring around the sides. Two round gold plated wires out the bottom, one longer than the other, hemispherical red lense, and designed to run at 0.020 amps. Not very bright by today's standards. I would gestimate a 30 degree viewing angle.
I remember making a cluster, six of these for a red flashlight. What impressed me was the lamp ran from a free Radio Shack 9 volt battery for more than a month with about 5 hours a week of use.
Mom didn't notice the red light, (very directional) that came from my room at night. I was reading science fiction when I was supposed to be sleeping.