Final answer:
To determine the focal length of the convex lens, we use the lens formula and the magnification equation. We find the image distance using the magnification and object distance, then substitute into the lens formula to solve for the focal length of the lens.
Step-by-step explanation:
The question asks for the focal length of a convex lens, given that a small insect 1.6 cm from the lens appears 2.5 times larger than its actual size. To find the lens's focal length, 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. Since the image is enlarged 2.5 times, the magnification m is -2.5 (it's negative because a convex lens produces a virtual image when the object is inside the focal length). Magnification is also the ratio of image distance to object distance, m = -di/do. By substituting the given values and solving for f, we can find the focal length of the lens.
Steps for calculation:
- Write down the magnification equation: m = -di/do
- Substitute the magnification (2.5) and the object distance (1.6 cm) into the equation to find the image distance di.
- After finding di, use the lens formula to solve for the focal length f.
After performing these calculations, we will have the focal length of the convex lens that magnifies the image of the insect by 2.5 times.