Final answer:
To find the distance of the image from the lens, the thin-lens equation is used with the given object distance and focal length. The image distance is calculated by rearranging and solving the equation using the provided measurements.
Step-by-step explanation:
To determine the distance of the image from the lens created by the convex lens, we can use the thin-lens equation: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance of the object from the lens, and di is the distance of the image from the lens. The sign convention has to be applied correctly to get the appropriate value for di.
Plugging in the given values:
- Focal length, f = 12.1 cm
- Object distance, do = 31.1 cm
We rearrange the thin-lens equation to solve for di:
1/di = 1/f - 1/do = 1/12.1 - 1/31.1
After calculating the values on the right side of the equation, we find the reciprocal to get di, the image distance.
The final calculation will yield the value for di, which is the answer to how far the image is from the lens.