What exactly is a 35mm single lens reflex camera?
Does a Nikon d40x come in that same category?
35mm is a film size. The most popular film size ever made. Since film is getting harder and harder to get, almost everybody has converted over to digital imaging. A 35mm single lens reflex camera is one where the "taking" lens is also used to record the image on the film. When a shutter is snapped/fired on a single lens reflex camera, the mirror used to reflect the image (what you see in the viewfinder) to your eyepiece, swings up out of the way and the film is exposed by what is known as a focal plane shutter. The mirror then returns to its original place reflecting the image up to the viewfinder. This all happens extremely fast. The shutter for your information is called a focal plane shutter because it travels directly in front of the film with a narrow slit in the shutter. And of course it is located at the focal plane of the camera. And the on digital cameras, film has been replaced by a "sensor".
Today 35mm film cameras are not made at all to my knowledge as digital photography has replaced film photography. Therefore the single lens reflex (SLR for short) of "yesterday" has become the Digital Single Lens Reflex (DSLR for short) of today. And the film has been replaced by a sensor which electronically records your image on a memory card.
A camera that uses 35mm film (not digital), has a single lens, and uses a mirror-reflex system to view what you'll take a picture of through the lens.
The D40x is a *digital* single lens reflex camera. It's the same as a 35mm single lens reflex camera, only instead of using 35mm film, it has a digital sensor. It's not a 35mm SLR.
A SLR camera is one where you look through the actual lens you use to take the picture. Other types of camera include rangefinders (where you have a viewfinder separate to the lens) or twin lens reflex, where there's a 'viewing lens' and a 'taking lens'.
The light path goes through the lens and is reflected, via a mirror, onto a pentaprism, which shows your the view in the viewfinder. When you take a picture, the mirror flips up and the light path goes straight through onto the film (film cameras) or sensor (digital cameras).So whilst the picture is being taken - all you see is black in the viewfinder.
35mm refers to the film size, and was a common size for film SLR cameras.
The Nikon D40x is a DIGITAL SLR or DSLR. It works the same way (mirror/pentaprism) but the light falls on a sensor, rather than film. It has a sensor smaller than the size of a 35mm negative (as do most consumer DSLR's) - so it's known as a crop sensor (or APS-C sized sensor).
The "35 millimeter" refers to the width of the film. It's certainly possible to make an SLR camera that shoots different-sized film, but they are fairly rare.