I'm assuming you mean "full frame" camera, and if so, then learning a few things about the cameras and lenses will help you understand why full-frame cameras can't use lenses intended for use on crop-frame bodies.
First... what's a "full frame" camera? Since the early days of photography, cameras have always produced images or negatives in different sizes. Over time these sizes started to standardize to certain sizes that were commonly used over and over.
The 35mm film standard was wildly popular -- even though there were still both larger and smaller film sizes available.
The 35mm size refers to the width of the film (not the size of the image). The film is wider than the image area to provide space for sprocket holes to make it easier for the camera to accurately advance the film. The area used for imaging was 24mm tall, but (usually) 36mm wide... a 2:3 ratio.
In the era of digital camera sensors, this size (24x36mm) becamse the size referred to as "full frame".
The problem with it was that when digital cameras were "new", a 24x36mm digital sensor was ludicrously expensive and very few people could afford one.
To make cameras more affordable, a slightly smaller sensor size was used (which would cut costs considerably) and the most common size for this was based on the size of APS-C film. APS-C stands for "Advanced Photo System - Classic" size. These were film cameras that used drop-in cartridges but the cameras often had some semi-futuristic (for that time) features where the camera could sense things such as the film sensitivity (ASA -- what we today refer to as ISO) and also the length of the film (the number of exposures). But this film was physically smaller.
Digital cameras were produced with these smaller "APS-C" size sensors which measure approximately 15mm tall by about 22mm wide (still maintaining the 2:3 image ratio). These cameras could be sold at a price low enough such that mere mortals could actually afford them.
Canon's latest line of 35mm film cameras were EOS cameras which used Canon "EF" series EOS lenses. So a digital camera that could still use those SAME Canon EOS lenses would have the advantage in that photographers could go from film to digital and not have to buy a completely new set of lenses. That sounds like a pretty good idea.
To this day, you can still put any Canon EOS "EF" series lens on ANY Canon EOS camera body (film or digital... full-frame or crop-frame... they all work.)
However... a lens projects an image into the camera body. Even though the film or sensor area is rectangular, the lens is (as you've certainly noticed) round. So the image being projected into the camera body is actually a circular image... the sensor (or film) happens to be positioned in the middle of that circular area. This means there really is some image that lands just above, below, left, and right of your frame. The important bit is that the diameter of this circle is "at least" large enough to cover the size of the image sensor. When measured diagonally, the sensor on a full-frame camera (or 36mm film) is just over 43mm wide. So as long as the lens produces an image circle which is at least that big, everything is fine.
There's no "problem" per se in using an EF lens on a camera that has a crop-frame (such as the popular APS-C size) sensor. It works well. But... it does mean you are using a lens which is over-engineered for what you're doing and things could be cheaper.
A large sensor needs a large lens (to cover the image area). When you pass light through glass, it disperses. How much it disperses depends on the angles of the glass where the light passes through. Most everyone understands that if you pass "white" light through a prism you get a rainbow of all the colors in the light. It turns out the edges of a single optical lens element work like a prism. To fix this, the lenses maker has to create corrective lens element to reverse the effect... it turns out they actually need several of these. The larger the diameter of the lens, the more work it takes to fix the problem.
If a lens were designed that only produced a smaller image circle, then that lens could have a smaller physical diameter. That would reduce the intensity of the dispersion problems and it would be easier to correct for these optical problems. Basically you can get a really high quality lens for less money (easier to make such a lens), not sacrifice quality, and the whole thing can be sold for less money. The lens is physically both smaller and lighter (it doesn't have as much "glass" inside it). It takes less space in your camera bag. You're not carrying around as much weight.
THAT is what a Canon EF-S lens is. It's a smaller lens that produces a smaller image circle. It costs less to build (becuase it doesn't need to cover a full-frame sensor). It still has high image quality (no sacrifices need to be made in that area to reduce the cost of the lens.)
When you buy a Canon T5i and it comes with the kit Canon EF-S 18-55mm f/3.5-5.6 STM lens... that's what you're getting is a lens that is designed to produce an image circle only large enough to cover the size of an APS-C sensor.
The diameter of that image circle only needs to be about 28mm... instead of the 44mm needed by the full-frame camera.
Now here's the problem....
If you were to try to attach an EF-S lens to a full-frame camera (and first, I should point out that it wont even fit... more on why in a moment) what you would discover (if it did fit) is that the images coming out of that camera would have a small circlular area in the middle of your image frame that had a visible image on it... and black edges and corners. You woudn't be happy with it.
Also... since the APS-C cameras have a smaller sensor, they also have a smaller reflex mirror that swings up every time you take a photo. Since the mirror is smaller, there's actually more empty space inside the camera (the sensor is just as far from the lens mounting flange as it is on full-frame bodies to guarnatee compatibility with full-frame lenses). Canon took advantage of the empty space and designed the EF-S lenses so that the rear-most lens element actually protrudes slightly into the camera body.
If you tried to mount such a lens (with a rear-element that sticks into the camera body just a bit) on a full-frame camera with a full-frame mirror, the mirror has a very high chance of smashing into the lens element because there isn't enough room for it to swing clear.
To prevent all of these bad things from happening to you, Canon altered the design of all camera bodies so that EF-S lenses cannot be attached to camera bodies that have full-frame sensors. They simply will not fit (on purpose) to avoid you damaing your camera by trying to use one.
This means that if you get a Canon camera with a full-frame sensor then you just use only Canon EOS "EF" lenses (without the "-S" suffix) or a 3rd party lens designed to be compatible wtih Canon full-frame bodies.
Tim Campbell
5D III, 5D IV, 60Da
