Final answer:
To find the final image position in a system comprised of a convex lens and a concave lens, we first calculate the image formed by the convex lens and then use it as an object for the concave lens, applying the lens formula for each step. The final image is virtual, on the same side as the object, and is located 10 cm from the concave lens.
Step-by-step explanation:
When an object is placed in front of a combination of a convex lens and a concave lens, the final image position can be found by analyzing the system in two steps. First, we find the image position due to the initial convex lens and then treat that image as the object for the concave lens. To find the position of the final image formed by the combined system, we will use the lens formula: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the object distance, and di is the image distance.
In this case, the object is 30 cm in front of the convex lens (do = 30 cm), which has a focal length of 10 cm (f = +10 cm). Calculating the image position due to the convex lens using the lens formula, we have:
1/10 = 1/30 + 1/di
Solving for di gives di = 15 cm. So the image formed by the convex lens is 15 cm behind it.
However, this image is now 5 cm in front of the concave lens (do' = -5 cm, because the image is on the same side as the object for the concave lens), which has a focal length of -10 cm (f' = -10 cm). Using the lens formula again for the concave lens:
1/-10 = 1/(-5) + 1/di'
Solving for di' gives di' = -10 cm. The negative sign indicates that the final image is on the same side as the object relative to the concave lens, 10 cm away from it.
Therefore, the final image formed by the combined system is virtual, on the same side as the object, and located 10 cm from the concave lens.