Final answer:
The distance between the two lenses is 46.31 cm, for a beam of parallel light, 1.70 mm in diameter passes through a lens with a focal length of 14.9 cm. another lens, this one of focal length 24.6 cm, is located behind the first lens so that the light traveling out from it is again parallel.
Step-by-step explanation:
To find the distance between the two lenses, we need to 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.
First, we need to find the image distance for the first lens. We can assume the object distance is infinite since the light is parallel. Therefore, 1/u = 0 and the formula simplifies to:
1/f = 1/v
Substituting the given values, we get:
1/14.9 = 1/v
Solving for v, we find that the image distance for the first lens is 14.9 cm.
Since the light is again parallel after the second lens, the image distance for the combined system is also 14.9 cm. Now, we can use the lens formula again to find the object distance for the second lens:
1/f = 1/v - 1/u
Substituting the given values, we get:
1/24.6 = 1/14.9 - 1/u
Solving for u, we find that the object distance for the second lens is 61.21 cm.
Finally, the distance between the two lenses is the difference between the object distance for the second lens and the image distance of the first lens:
61.21 cm - 14.9 cm = 46.31 cm