Final answer:
To find the focal length of the second lens and the distance between the original object and the final image, we use the thin lens equation and magnification concepts step-by-step, considering the properties of the image formed by the first lens and the relationship of the final image to this intermediate image.
Step-by-step explanation:
To find the focal length of the second lens if the final image is inverted and has a height of 5.60 mm given an initial object height of 4.00 mm positioned 28.0 cm to the left of a converging lens with a focal length of 8.40 cm, we will first determine the properties of the image formed by the first lens using the lens equation and magnification. To find the distance between the original object and the final image, we then consider the object-image distance for each lens separately.
Steps to solve the problem:
Step 1: Use the thin lens equation 1/f = 1/do + 1/di to find the image distance (di) produced by the first converging lens.
Step 2: Determine the magnification (m) of the first image using the formula m = -di/do, which also gives the height of the first image.
Step 3: The first image acts as the object for the second lens. Use the given final magnification to find the object distance for the second lens, considering the spacing between the lenses.
Step 4: Using the magnification formula for the second lens and the found object distance, calculate the focal length of the second lens.
Step 5: To find the total distance between the original object and the final image, add the object distance from the first lens and the image distance from the second lens, accounting for the spacing between lenses.