A ‘normal’ lens is one that produces a ‘normal’ perspective. It’s one that is similar to the human eye. A scene depicted using a normal lens will appear to have a natural and undistorted view. In fact normal lenses are quite close to the human eye in terms of image perspectives. Nevertheless, what is normal for one individual may be different for another. Given this apparent disagreement a convention has been adopted.
In photography a lens with a focal length of the same length as the diagonal across a 35mm digital sensor will be a normal lens. As the diagonal across a 35mm (full frame) sensor is 43mm the most practical sized lens to match that focal length is a 50mm lens. There is also a little history to this choice too. So, for the sake of convention the 50mm standard has been pretty universally accepted.
The 50mm lens creates an aesthetic and effective/representative image close to that of the human eye. However, it only does so on a 35mm sensor. Smaller cropped sensors form the majority of digital image sensors and these have the effect of cropping the image by a fixed amount called the crop factor. The crop factor varies between brands. So before considering what may be normal for your lens you will have to adjust for the crop factor your camera applies.
A 50mm lens when affected by a crop factor of 1.6 (Canon ASP-C format cropped sensor) gives an effective focal length of 80mm (50 x 1.6 = 80) which is within range of a pleasing perspective for a normal lens. In addition, the most aesthetic focal length for portraits is considered to be 85mm. So, give or take a few millimetres, the cropped sensor cameras using a 50mm lens are within both an aesthetic and effective range of that considered as ‘normal’. Other crop factors for different cameras and manufacturers vary, but there is not a huge variance in DSLR sensor sizes. For the purposes of the ‘normal’ lens calculations there is only a few millimetres of focal length difference between them. I acknowledge that these arguments are aesthetic and not bound to physical measurement. However, in terms of the outcome of an image it is perhaps aesthetic concerns which should be taken the most seriously.