Final answer:
The thin-lens equation, 1/do + 1/di = 1/f, can be derived using a ray-tracing diagram and relates object distance, image distance, and focal length of a lens. It helps in determining the characteristics and magnification of the image formed by the lens.
Step-by-step explanation:
True, the thin-lens equation 1/do + 1/di = 1/f can indeed be derived using another ray-tracing diagram for the given situation. This equation relates the object distance (do), the image distance (di), and the focal length (f) of the lens. To derive the thin-lens equation, consider an object being refracted by a lens.
The image formed by the first refracting surface (the left surface of the lens) is used as the object for the second refracting surface. You extend the rays backwards from inside the lens to find this first image, which we'll call Q'. Though Q' is a virtual image, we can still determine the image distance d for it.
Once we know the distances of the object (do) and the image Q' (d), we can insert these values into the lensmaker's equation. Thin lens equations are also essential for predicting the characteristics of the image formed, whether it's real or virtual, and the magnification (m) of that image. Ray tracing complements numerical solutions provided by the thin lens equation, enhancing the understanding of the image formation process.