Final answer:
Images formed by convex and concave lenses differ in nature, position, and size depending on the object's distance from the lens and the lens's focal length, using the lens equation and ray tracing to predict these characteristics.
Step-by-step explanation:
The nature, position, and relative size of the image formed by convex and concave lenses can be determined using the principles of geometric optics. When an object is placed at various distances from the lens, the characteristics of the image such as whether it is real or virtual, upright or inverted, and magnified or diminished, can change based on the focal length of the lens and the position of the object relative to this focal point.
For a convex lens, real, inverted images are formed when the object is placed beyond the focal point, virtual, upright images are formed when the object is within the focal length. As for a concave lens, it always forms virtual, upright, and reduced images irrespective of the object position.
To predict the exact image characteristics, we use the lens equation 1/f = 1/o + 1/i, where f is the focal length, o is the object distance, and i is the image distance. We can also use ray tracing methods to visually determine image location and size.