Answer :
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.
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.
Final answer:
The focal length of the second lens is determined using the thin-lens equation and magnification calculations, while the total distance between the original object and the final image includes distances involving both lenses.
Explanation:
Solution for Part A
Firstly, using the thin-lens equation 1/f = 1/do + 1/di for the converging lens with object distance do = -28.0 cm (negative indicates object is on the same side as the incoming light) and focal length f = 8.40 cm, we find the image distance di. Then, we calculate the magnification m using m = -di/do, where the negative sign indicates the image is inverted.
Once we have the magnification for the first lens, we can use it to find the object distance for the second lens, as the image created by the first lens becomes the object for the second lens. The magnification of the second lens must also account for the change in size from 4.00 mm to 5.60 mm. We again use the lens equation for the second lens to solve for its focal length f2 since we seek an inverted image (negative di for the second lens).
Solution for Part B
The distance between the original object and the final image is the sum of the object distance to the first lens, the distance between the two lenses, and the image distance from the second lens (with appropriate signs to indicate direction).
