Final answer:
To determine the focal length of the lens, use the lens maker's formula. To determine whether the lens is converging or diverging, use the sign convention for focal length. To determine the image distances for different object distances, use the thin lens formula.
Step-by-step explanation:
The focal length of a lens can be determined using the lens maker's formula, which states that 1/f = (n - 1)(1/R1 - 1/R2), where f is the focal length, n is the index of refraction of the lens, and R1 and R2 are the radii of curvature of the lens surfaces.
Substituting the given values into the formula, we have 1/f = (1.64 - 1)(1/(-10.5) - 1/35.0). Solving for f gives us the focal length of the lens in centimeters.
To determine whether the lens is converging or diverging, we can use the sign convention for the focal length. If the focal length is positive, the lens is converging, and if the focal length is negative, the lens is diverging.
The image distance for an object distance can be determined using the thin lens formula, which states that 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.
Substituting the given values into the formula, we can calculate the image distances for object distances of infinity, 6.00 cm, and 60.0 cm.