Final answer:
Using the lens formula, the image formed by a positive lens with a focal length of 9 cm for an object placed 24 cm away is located 14.4 cm from the lens, indicating a real image on the opposite side of the lens.
Step-by-step explanation:
The question asks us to determine the image distance when an object is placed 24 cm from a positive lens (converging lens) with a focal length of 9 cm. To find the image distance, we can use the lens formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. In our case, the focal length is 9 cm, and the object is located 24 cm from the lens, so we have:
1/9 = 1/24 + 1/di
Solving for di, we get:
1/di = 1/9 - 1/24
1/di = (24 - 9)/(9×24)
1/di = 15/(9×24)
1/di = 15/216
1/di = 5/72
di = 72/5
di = 14.4 cm
The image is located at 14.4 cm from the lens, where the image distance is positive, indicating that the image is real and located on the opposite side of the lens from the object.