Converging Lenses and Ray Diagrams

A converging lens is thicker in the middle than at the edges, so it bends light rays toward a central axis. Every lens has a focal length f, the distance from the lens to the point where parallel rays crossing it all meet. To find an image, draw three rays from the tip of the object: one parallel to the axis that bends through the far focal point, one through the center of the lens that goes straight (the lens is thin there, barely bending it), and one through the near focal point that leaves the lens parallel to the axis. Where these three rays cross on the other side is the image of that point. Do this for the base of the object too, and you have the whole image.

As you slide the object closer to the lens, the image behaves in stages. Far outside the focal length, the image is real, inverted, and smaller or similar in size, forming on the opposite side of the lens where light actually converges. As the object approaches the focal point, the image moves farther away and grows larger. Once the object sits inside the focal length, the rays no longer converge on the far side at all — they spread apart, and the image becomes virtual, upright, and magnified, appearing on the same side as the object. This is exactly the magnifying glass case: hold it too close or too far and the image is blurry or inverted, but at the right distance outside the focal length, sunlight converges to a tiny bright point hot enough to burn.

The same ray-tracing logic connects directly to the thin lens equation, 1/do + 1/di = 1/f, which gives the exact numbers the rays only sketch. It also explains the half-covered lens: rays still arrive from every lens point, so the image survives, just dimmer.