Fish Eye (Wide Angle) Lens

The "fish eye" or wide angle lens allows an image show an increased field of view by projecting the image into a sphere. This is best explained with a picture:

Here we see a sphere in a box. There are some other primitives, but they are far off to side and we can only glimpse a corner of each.
When we use the fish eye lens, we get this:

Suddenly the shapes that were to far outside the field of view are now visible. Note that the sphere looks perfectly normal, although farther away, while the objects on the sides look curved around the edges of a sphere. I added a small fade to black around the edges for effect. The above image was rendered with 40 degrees field of view. This following one is the same image, only with 80 degrees field of view: