How does a round camera lens produce a square picture?

something i've never figured out, is how the picture and the film is square, but the lens is round. anyone know?

The lens produces a round image, but the part that captures the image (the sensor or film) is square. So, you get to keep only a portion of what the camera saw. The square fits neatly inside the round imaging circle. If you somehow loaded a camera with a special circular film, you could conceivably get round photos, but it isn't practical. Lens tend to get soft at the edges. Not only is it much easier to make square image sensors and square film, but the camera gets the best part of the image. Even on today's top end cameras, the edges will tend to not be as sharp.

Film is easier to make in strip than circle, and square film crops the beginning circular image. With digital it's a wafer in rows, cut in lines. Chips are square, wafers are round. Wafers are made by slicing crystal semiconductor starter into cylinders. Do to crystal growing, this results is round flat wafers. Of course you can put a fish eye lens on a cam and have a round image with a black area surrounding. Really the answer your looking for is the medium exposed is square, and the capturing device circle. Kinda like the kids toy where you put a triangle, square, circle in matching holes. The technology is there to have a "round" image(take imax for example), though costly. When you take this question and move it to a video level you have frames that mesh to form a a curved moving image. If your device was say a holographic imaging system, and your medium digital data, all you'd need is a spherical lens. Beyond that is 4d space, a tesseract device would come into play, to capture space time you'd need a box containing the 4d space your capturing. To capture it on the go, you'd need a true tesseract capturing device, spliting our space in 4 cubes, inside a cube, inside a cube. That's called a hypercube.

The lens produces not picture. It merely focuse and gathers light.

It is the film, or the digital diode array that make the picture. Both the film and the array are in rectangular format. So, some of the light gathered by the lens never makes it to the camera back. It gets "cropped" off.

It would work on round film, too. It's just easier to make square film and be sure the lens can cover it. Some of the round image is "wasted."