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Suppose I have a sheet of cardboard, or for that matter any irregularly shaped object. Now we do know that reflection on cardboard is irregular and not specular as it is a rough surface compared to a mirror. So when our eyes intercept the light rays, how do we get an image that is not distorted and it preserves the geometry of the shape. My thinking is that since the reflected rays are not parallel, how are our eyes able to make out the object accurately, same goes for cameras.

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I think you have a misunderstanding of how lenses form images (misleading diagrams in physics text books)

Of the many rays reflected at random directions from the cardboard, some will go toward your eye, all the rays coming from the same point are parallel and so will be focussed to the same point in the image. The same then applies for a nearby point on the object, making a nearby point on the image, and so on. Obviously only the ones that enter your eye form an image.

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