Lenses are classified as to wide-angle, “normal” or telephoto based on what focal length is considered “normal” for the camera’s format. The compact digital was spawned from what was billed as an advanced photo system. This is the failed APS system of the 1990’s based on 24mm wide film. The image area is 16mm height by 24mm length. A “normal” focal length for any format is approximately the diagonal measure of the frame. For the compact this is 28.8mm. The industry generally rounds this value up to 30mm. Such a lash-up delivers an angle of view of 45° with the camera held in the horizontal. However the often quoted angle is 53°, this is taken from the diagonal measure (like TV’s are sold by their diagonal size.
As a rule of thumb, a lens 70% of “normal” = 20mm or shorter fall in the realm of wide-angle. As focal length decreases, the angle of view increases. As the focal length is made shorter and shorter, sooner or later it won’t work. This is because the back end of the lens barrel must poke deep into the interior of the camera. What happens is, interference with the SLR mirror and maybe the shutter. To mediate, the wide-angle must be somehow positioned more forward. Now comes some problems. To obtain good illumination over the entire area of the sensor/film, If the angle of view is super wide (80° or more), the center area of the picture area will be 4X brighter than at the margins (law of cos4). Now comes complex optical design to mitigate this vignette. Now the lens maker falls back to a making a unsymmetrical lens.
The short back-focus of the wide angle must also be handled. Retrofocus to the rescue: This is actually an inverted/reverse telephoto. This design uses an upfront diverging lens and a rear convergent lens. This shifts the focal length measuring point forward and this allows the lens barrel to be positioned forward so mirror and shutter of the SLR are given clearance. The additional back focus distance helps to mitigate the vignette of the wide-angle.
The telephoto realm is 2X “normal” or longer. This will be 60mm or longer for the compact digital. As the focal length increases, so does the barrel length. Unless the lens design is somehow changed, the extra length makes the lens awkward to use. A negative lens element placed behind the upfront positive changes an otherwise long lens design into a telephoto. This is a long focal length in a shorter lens barrel. The arrangement of the lens components shifts the point of focal length measuring making the barrel more compact.
Consider the engineering and the elevated production cost of making a Retrofocus and a true telephoto.