Final answer:
Using the thin-lens equation and the given focal length of 24 cm, it is found that the image distance is 48 cm when an object is placed 16 cm from the lens. The image is virtual and located on the same side of the lens as the object.
Step-by-step explanation:
To determine the image distance when an object is placed 16 cm from a thin converging lens, we can use the thin-lens equation:
\(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\)
Where f is the focal length of the lens, d_o is the object distance, and d_i is the image distance.
We are given that an image forms at 24 cm when an object is at infinity, so the focal length f is 24 cm. Now we can plug in the given object distance of 16 cm.
\(\frac{1}{24 cm} = \frac{1}{16 cm} + \frac{1}{d_i}\)
Solving for d_i, we get:
\(\frac{1}{d_i} = \frac{1}{24 cm} - \frac{1}{16 cm}\)
\(\frac{1}{d_i} = \frac{2 - 3}{48 cm}\)
\(\frac{1}{d_i} = -\frac{1}{48 cm}\)
d_i = -48 cm
The negative sign indicates that the image is virtual and on the same side of the lens as the object. Therefore, the image will form 48 cm from the object on the same side as the object.
The correct answer is C. 48 cm.