The camera lens projects a circular image of the outside world onto the surface of film or digital sensor. Most modern cameras are designed around a rectangular format. This rectangle, known as the “classic format”, has a length that is 1 ½ times height. As an example, the full frame (FX) measures 24mm height by 36mm length. The now popular compact digital (DX) has a format that is 66% of this size. The DX measures 16mm by 24mm. This classic format, when enlarged, exactly matches to make a 4X6 inch print or an 8x12 inch print.
Now the camera lens projects a circular image aimed so that it focuses on the flat surface of film or digital sensor. Only the center portion of this projected circle is photographically useful. The central portion is called the “circle of good definition”. Beyond this image circle, the image is too dim and too blurred to be useful. To retain only the useful central potion, the camera is equipped with baffles and a format mask. It is this mask that sets the format size.
The typical camera lens is designed for a specific format dimension. This is especially true when it comes to short focus lenses. This is because short, wide-angle lenses must be positioned close to film or digital sensor. It is this closeness that is the peril. If the back-focus is short, there is but minuscule space for the lens mounting mechanism. This is especially bad if the camera has a mirror imposed between lens and image plane. To get around this, a trick used is: Make the lens retro-focus. In this design, the focal length measuring point, called the rear nodal, is shifted rearward. This scheme allows for a longer back-focus distance. The longer back-focus, plus clever use of multiple lens elements of different shapes and powers, enlarges the useful diameter of the circle of good definition. What I am trying to say is, short focus, (wide-angle) lens are challenging.
For the above reasons and some others not covered, the focal length considered “normal” for any camera is a lens with a focal length about equal to the corner to corner measure (diagonal measure) for the format. For the FX (full frame 35mm) that’s about 45mm. This value is usually rounded up to 50mm by tradition. For the DX (compact digital) that’s 30mm. By definition, a “normal” is a lens that delivers a view that is not wide-angle and not telephoto.
Key to your question is – If a “normal” lens is fitted to a camera, the angle of view will always be 53°. This is the angle of view that is most often published. This is the diagonal angle of view. With a camera sporting a classic format held in the landscape orientation, fitted with a “normal” lens, the angles of views realized, are 53° diagonal, 45° horizontal, and 31° vertical. Again, this is true for all cameras sporting a “normal” lens coupled with a classic format (length 1.5 times height). Now the angle of view expands when a shorter lens is fitted and shrinks when a longer lens is mounted.
If the camera sports a classic format rectangle and we know the crop factor, we can easily find the format dimensions. For the Power Shot, 2.7 crop factor: Sensor dimensions are 24 ÷ 2.7 = 8.8mm height --- 36 ÷ 2.7 = 13.2mm length, diagonal 15.9mm. Angle of view when fitted with “normal 15.9mm” = 31° vertical 45° horizontal 53° diagonal.
For the Panasonic Lumix DMC-GX8 crop factor 2:
Format 12mm height 18mm length 21.6 diagonal
Angle of view when fitted with “normal 21.6” = 31° vertical 45° horizontal 53° diagonal.
When it comes to “normal” we can’t get away from these angles of view unless we use a lens other than “normal”, or a format dimension that departs from the classic rectangle. Most cameras mount a “normal” or kit lens zoom centered on “normal”.