In article <3vhh0t$8gl@net.auckland.ac.nz>, boonl@ccu1.auckland.ac.nz
says...
>
>If a 15mm lens has an angle view 180 degrees, why does a 14mm
>lens have a angle view of 114 degrees?

Actually, any lens up to about 17mm can cover 180 degrees in the
35mm format if it uses a lens design formula that results in a
spherical perspective image, rather than a rectangular perspective
image. In spherical perspective, straight lines in the subject that
do not run through the center of the image are rendered as curves.
The farther from the center, the more curved they are - like
longitudinal lines marked on a globe appear when you view the
globe straight over the equator. Two 15mm lenses, one rendering
spherical and the other rectangular image perspective, will show
the same image size in the center of the image, but the spherical
(fisheye) lens will show ever smaller image size as you approach
the edge of coverage, thus allowing more to be included (it shows
a wider angle of view). Fisheyes have been made by Nikon down
to about 6mm in focal-length, and these can cover 220 degrees.
An interesting sidelight is that the rules of the two types of
perspective show that we see in fisheye perspective (Darn hard
to convince clients of that!). Fisheyes permit the imaging of
angles which can exceed 180 degrees, but which have focal-lengths
greater than zero, and can therefore exist. The rules of
rectangular perspective dictate that as the angle-of-view
approaches 180 degrees, the focal-length approaches zero - a lens
that cannot exist! Hope this helps.