If you have ever looked at the lens of a magnifying glass, you know it is thick in the middle and tapers to nothing at the edges. In other words it is shaped like a lentil, which is where the word lens comes from. It would not be very easy to make a big magnifying glass lens for your RV because it would be thick, heavy and hard to mount.
The thin piece of plastic you are using is called a fresnel lens. It is flat on one side and ridged on the other. Fresnel lenses we first used in the 1800's as the lens that focuses the beam in lighthouse lamps. Plastic fresnel lenses are used as magnifiers when a thin, light lens is needed. The quality of the image is not nearly as good as that from a continuous glass lens, but in lots of applications (like your RV) perfect image quality is not necessary.
The basic idea behind a fresnel lens is simple. Imagine taking a plastic magnifying glass lens and slicing it into a hundred concentric rings (like the rings of a tree). Each ring is slightly thinner than the next and focuses the light toward the center. Now take each ring, modify it so it flat on one side, and make it the same thickness as the others. To retain the rings' ability to focus the light toward the center, the angle of each ring's angled face will be different. Now if you stack all the rings back together, you have a Fresnel lens. You can make the lens extremely large if you like. Large fresnel lenses are often used as solar concentrators.
The following links are useful: