Final answer:
To find the new image distance for a different converging lens, the thin-lens equation is used. For the lens with a focal length of 15.0 cm, with the object distance calculated based on the initially given parameters, the new image distance is approximately 41.25 cm.
Step-by-step explanation:
The student has asked about the image distance when an object remains in the same position but the converging lens is changed. To determine the new image distance after replacing the first converging lens with another converging lens that has a different focal length, we can use the thin-lens equation given by:
1/f = 1/do + 1/di
Where f is the focal length of the lens, do is the object distance, and di is the image distance. Since the object distance remains the same, the value of do is unchanged when the lens is replaced.
For the first lens with focal length 14.0 cm and image distance 24.0 cm, we have:
1/f1 = 1/do + 1/di1
Rearranging the formula to solve for do, we get:
1/do = 1/f1 - 1/di1
Substitute the known values:
1/do = 1/14 - 1/24 ≈ 0.05714 cm
-1
Because the object distance is a positive quantity for real objects, we take the reciprocal of this value to find do:
do ≈ 17.5 cm
Now, using the second lens with focal length 15.0 cm and the same object distance, we apply the thin-lens equation to find the new image distance di2:
1/f2 = 1/do + 1/di2
Solving for di2 gives us:
di2 = 1/(1/f2 - 1/do)
Substitute the known values:
di2 = 1/(1/15 - 1/17.5)
After calculating, we find:
di2 ≈ 41.25 cm
So, the new image distance for the second lens is approximately 41.25 cm.