Final answer:
To determine the focal length of a biconvex lens that creates a virtual image 2.6 times the size of an object 2.18 cm away, we use the lens formula along with the given magnification. The calculation reveals that the focal length is approximately -1.18 cm.
Step-by-step explanation:
To find the focal length of the lens when a biconvex lens forms a virtual image 2.6 times the size of the object, and the object distance is 2.18 cm, 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. Because the image is virtual and magnified, the image distance di is negative and we know that magnification (m) = -di/do. Given the magnification is 2.6, we can express di as -2.6 * 2.18 cm. Substituting this into the lens equation, we calculate the focal length.
To solve for f, we now have:
- Object distance (do) = 2.18 cm
- Image distance (di) = -2.6 * 2.18 cm
- Magnification (m) = 2.6
By substituting the values into the lens formula, we get:
1/f = 1/2.18 cm + 1/(-2.6 * 2.18 cm)
After calculating, we find that the focal length (f) of the lens is approximately -1.18 cm.