Final answer:
For a spherical convex mirror with a radius of curvature of 40.0 cm, we can determine the position of the virtual image and the magnification for object distances of 30.0 cm and 60.0 cm. The image for an object distance of 30.0 cm is 58.8 cm away from the mirror and is inverted. The image for an object distance of 60.0 cm is 30.3 cm away from the mirror and is upright.
Step-by-step explanation:
To determine the position of the virtual image and the magnification for different object distances, we can use the mirror formula:
1/f = 1/do + 1/di
where f is the focal length of the mirror, do is the object distance, and di is the image distance.
For a spherical convex mirror with a radius of curvature of 40.0 cm, we can determine the focal length by dividing the radius of curvature by 2. Hence, the focal length is 20.0 cm.
Using the mirror formula, we can substitute the values to calculate the image distance and magnification for each object distance:
i) do = 30.0 cm:
1/20.0 = 1/30.0 + 1/di
0.05 = 0.033 + 1/di
1/di = 0.05 - 0.033 = 0.017
di = 1/0.017 = 58.8 cm
The image distance for an object distance of 30.0 cm is 58.8 cm. To determine the magnification, we can use the formula:
magnification = -di/do
magnification = -58.8/30.0 = -1.96
The magnification is -1.96, which indicates that the image is inverted.
ii) do = 60.0 cm:
1/20.0 = 1/60.0 + 1/di
0.05 = 0.017 + 1/di
1/di = 0.05 - 0.017 = 0.033
di = 1/0.033 = 30.3 cm
The image distance for an object distance of 60.0 cm is 30.3 cm. To determine the magnification:
magnification = -30.3/60.0 = -0.505
The magnification is -0.505, which indicates that the image is upright.