Final answer:
To find the final image distance, we first calculated the image distance for a diverging lens with the lens formula, 1/f = 1/do + 1/di, which turned out to be -20 cm. This virtual image acts as an object for the second lens, and after applying the same formula with given values, the final image distance from the second lens is found to be 13.33 cm, which is real and located on the opposite side of the lens.
Step-by-step explanation:
To find the final image distance from the second lens, we first need to determine the image formed by the first diverging lens and then use that image as an object for the second converging lens.
We can use the lens formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.
Step 1: Locate the image formed by the diverging lens.
- First, we apply the lens equation to the diverging lens. Since it's a diverging lens, its focal length is negative, f = -15 cm.
- Using the object distance do = 60 cm (object distance should be positive), we solve for the image distance di:
1/f = 1/do + 1/di
1/(-15) = 1/60 + 1/di
1/di = 1/(-15) - 1/60
di = -20 cm (A negative image distance indicates that the image is virtual and located on the same side of the lens as the object)
Step 2: Locate the final image formed by the converging lens.
- The image formed by the diverging lens will serve as the virtual object for the converging lens.
- Since the lenses are 10 cm apart, the object distance for the second lens is do' = di + 10 = -20 + 10 = -10 cm.
- Applying the lens equation to the converging lens with f = 20 cm, we find the final image distance di':
1/f = 1/do' + 1/di'
1/20 = 1/(-10) + 1/di'
1/di' = 1/20 - 1/(-10)
di' = 13.33 cm (The positive image distance indicates that the image formed by the second lens is real and located on the opposite side of the converging lens from the object)