Great question! To determine the image size and distance from the lens, we can 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.
Given that the focal length (f) is 4.0 m and the object distance (u) is 12.0 m, we can substitute these values into the formula:
1/4 = 1/v - 1/12
To solve for v, we need to rearrange the equation:
1/v = 1/4 + 1/12
1/v = (3 + 1)/12
1/v = 4/12
1/v = 1/3
Now, we can find the value of v by taking the reciprocal of both sides:
v = 3 meters
So, the image distance (v) is 3 meters.
To find the image size, we can use the magnification formula:
magnification (m) = -v/u
Given that the object height (h) is 2.0 meters, we can substitute these values into the formula:
m = -v/u = -3/12 = -1/4
The negative sign indicates that the image is inverted. The magnification value of -1/4 means that the image is one-fourth the size of the object.
Therefore, the image size is 1/4 of the object's height, which is 1/4 * 2.0 = 0.5 meters.
So, the image size is 0.5 meters and the image distance is 3 meters from the convex lens.
I hope this explanation helps! Let me know if you have any further questions.