Final answer:
The focal length of the lens is calculated using the lens formula, and with the given distances, the focal length is found to be -200 cm. However, this doesn't match the options provided, suggesting a typo in the question or the answer choices.
Step-by-step explanation:
To determine the focal length of the thin lens, we can use the lens formula, which is 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance of the object from the lens, and di is the distance of the image from the lens. In the given scenario, the object distance (do) is 40 cm, and the image distance (di) is -50 cm (negative because it's a virtual image and on the same side as the object).
Plugging in the values, we get:
1/f = 1/40 + 1/(-50),
1/f = -1/200.
Thus, f = -200 cm.
However, the only negative value among the options provided in the question is -45 cm, which indicates that there may be a typo in the question or among the answer choices.