A "normal" lens was originally defined as a lens that reproduces a similar field of view that an eye would naturally see. And at some point it was determined that a 50mm lens reproduced approximately what a human eye would "normally" see.
This is the way that I learned it, too.
If you were to position 2 people with a 50mm lens--one being 10 feet in front of the other so one person is closer to the camera--and were to take their photo by standing 10 feet in front of the closet person, the distance between them would appear to look the same as it does with the naked eye. If you were to take their photo with a 35mm lens, the photo would appear to have a greater distance between them than really existed. And if you were to take their photo with a telephoto lens (say 85mm), it would compress the distance between them making them appear to be standing closer together than they really are.
When you factor in a DX camera body, you don't change those perspectives. All the camera does it to seemingly take a photo like it would on an FX body and CROP the picture after-the-fact--like cropping off the outside edges of a photo if it was taken on an FX body.
Wide angle lenses push things away making them appear further from the camera than they really are while telephoto lenses make things appear closer together and closer to the camera than they really are. The perspective of normal lenses (whether DX or FX) look just as 'real' or identical to how things look with the naked eye.
If you want to see firsthand what I mean, go find 2 telephone poles and photograph them 3 ways by standing in the same place for all 3 pics--with a wide angle, normal, and telephoto lens. Be sure to photograph them by having one closer to the camera than the other.
Notice how the actual phone lines look when comparing the photos, and you will see how the perspective changes. The same perspective will show up no matter whether you are using a DX or FX camera.
