For valid reason, which I will explain later, the “normal” focal length for any size camera is a focal length that is approximately the same length as the diagonal measure of its format size. Additionally, the aspect ratio of most rectangular format cameras is 3÷2 = 1.5. In other words, the length is 1.5 times the height.

If you mount a lens, focal length equal to the diagonal measure, the angle of view delivered is 53°. This is the most often quoted angle of view, somewhat like the fact that TV sets are sold by their diagonal measure.

If the camera’s aspect ratio is 3:2, and the lens focal length equals the diagonal measure, the angle of view, camera held horizontally will be approximately 45°.

A lens is generally considered to be wide-angle if its focal length is about 70% of “normal” or shorter. A lens twice “normal” or longer falls into the realm of telephoto.

Why is a “normal” lens one that is about equal to the hypotenuse of the format rectangle?

All lenses project a circular image. Only the central portion of this image is suitable photographically. Additionally, this image is vignetted (a dimming of the edges). The central portion is called “the “circle of good definition”. For these reasons, the camera masks off this circular image, creating a rectangular format or frame size.

Now the rest of the story: We see with our eye/brain combination. We perceive what we call “the human perspective”. This is the 3D vision we are blessed with. We judge the relationships of objects by how we perceive them as to their size and distance. A “normal” lens is one that roughly replicates the “human perspective”.

If we were to view a vista through a glass windowpane, we can trace the outline of objects on the glass with wax pencil. We can also image this scenery using a camera. We then view the picture we have made. If we view this image from a distance equal to the focal length of the taking lens, we will perceive that this image replicates the “human perspective”.

Such a viewing distance is likely impossible given that today’s cameras are small devices fitted with short lenses -- plus the closest we can focus with our unaided eye is 6 inches / 150mm. Also, we tend to look at pictures from a distance about equal to their diagonal measure.

Suppose you take a picture with a full frame 35mm camera and view an 8x10 print made from that image. The 8x10 inch print is an enlargement, magnification 8X. To view a picture and perceive via the “human perspective”, the math is --- viewing distance is the focal length of taking lens multiplied by magnification. For this image, the viewing distance for a “normal” 50mm lens is 50 X 8 = 400mm = 16 inches, about normal reading distance. The APS-C requires 12X magnification, the normal lens is 30mm thus 30 X 12 = 360mm = 14 inches viewing distance. See how this all works out to the “human perspective”.

The macro lens is one that is optimized to work in close, we are talking live-size = 1:1 meaning magnification 1. No such formula, thus the lens specifications.