Question

Two converging lenses are placed 36.0 cmcm apart. The focal length of the lens on the right is 20.5 cmcm , and the focal length of the lens on the left is 10.5 cmcm . An object is placed to the left of the 10.5 cmcm focal-length lens. A final image from both lenses is inverted and located halfway between the two lenses. How far to the left of the 10.5 cmcm focal-length lens is the original object?

Answer 1

Using the thin-lens equation and the given parameters, the object distance from the first lens can be computed in steps, first finding the image distance from the second lens and then backtracking to the original object position.

Step-by-step explanation:

The question involves a scenario with two converging lenses and requires the application of the thin-lens equation to determine the object distance from the first lens. The final image is located halfway between the two lenses, which are 36.0 cm apart. Therefore, the image distance from each lens is 18.0 cm. We can use the lens equation 1/f = 1/do + 1/di to find the object distance (do) for the first lens.

For the lens on the right with a focal length of 20.5 cm and an image distance of 18.0 cm, the object distance from this lens, which serves as the image distance for the first lens, can be found using the lens equation. Plugging in the values, we get 1/20.5 = 1/do + 1/18.0. Solving for do gives us the object distance from the second lens. We can then use the object distance from the second lens, combined with the distance between the two lenses, to determine the original object distance from the first lens with a focal length of 10.5 cm, again using the lens equation.