The distance between the object and the image is approximately 36cm.
Here's how to calculate it:
1. Use the magnification formula to find the image distance:
m = -i/o = v/u
where m is the magnification, i is the image distance, o is the object distance, v is the image height, and u is the object height.
Given that the image is upright and three times the size of the real object, we have:
m = v/u = 3
2. Use the lens formula to find the image distance:
1/f = 1/i + 1/o
where f is the focal length of the lens.
Substituting the given values, we get:
1/0.12 = 1/i + 1/o
3. Substitute the magnification formula into the lens formula to eliminate the object distance:
1/0.12 = 1/i + 1/(3o)
4. Solve for the image distance:
i = 0.24 m
5. Use the magnification formula to find the object distance:
m = -i/o = v/u
Substituting the given values, we get:
3 = v/u = -i/o = -0.24/o
o = -0.08 m
6. Calculate the distance between the object and the image:
d = i + o = 0.24 m + (-0.08 m) = 0.16 m = 16 cm
Therefore, the distance between the object and the image is approximately 36 cm.