Final answer:
The position of the final image is 20 cm to the right of the second lens, and its magnification is -1.
Step-by-step explanation:
In this question, we have two convex lenses and an object placed between them. The first lens, lens A, has a focal length of 20 cm, and the second lens has a focal length of 10 cm. The object is placed 10 cm to the left of lens A. To find the position of the final image, we can use the lens formula:
1/f = 1/v - 1/u
where f is the focal length of the lens, v is the image distance, and u is the object distance. Since the object is placed between the two lenses, the image formed by lens A will act as the object for the second lens. We can find the image distance and magnification for each lens separately and then combine them to find the final image.
Using the lens formula for lens A:
1/20 = 1/v - 1/10
Solving this equation, we find that v = 20 cm. So, the image formed by lens A is located at 20 cm to the right of lens A.
Now, we can consider this image as the object for the second lens. Using the lens formula for the second lens:
1/10 = 1/v' - 1/20
where v' is the distance of the final image from the second lens.
Solving this equation, we find that v' = 20 cm. So, the final image is located 20 cm to the right of the second lens.
To find the magnification of each lens, we can use the formula:
magnification = -v/u
where v is the image distance and u is the object distance. Using this formula for lens A, we find that the magnification is -20/10 = -2.
For the second lens, the object distance (u') is 20 cm and the image distance (v') is 20 cm. Using the formula, we find that the magnification is -20/20 = -1.
Since the final image is formed by the second lens, the magnification of the final image is -1.
Therefore, the position of the final image is 20 cm to the right of the second lens, and its magnification is -1.