A spherical Christmas tree ornament is
5.34 cm in diameter.
What is the magnification of the image of
an object placed 10.3 cm away from the ornament
The focal length is f = -R/2 = -1.33 cm
The object distance is do = 10.3 cm
1/10.3 + 1/di = 1/f = -1/1.33
Solve for image distance, di. It will be negative (behind the ornament)
Magnification = |di/do|
To calculate the magnification of the image formed by the spherical Christmas tree ornament, we can use the formula:
Magnification (m) = - (image distance / object distance)
Given:
Object distance (u) = 10.3 cm
Since the ornament is a convex lens, the image formed will be on the opposite side of the object, and it will be virtual (since the object distance is less than the focal length).
The focal length (f) of a convex lens can be calculated using the formula:
f = (radius of curvature) / 2
Since the ornament is a sphere, the radius of curvature is equal to half the diameter.
Radius of curvature (r) = 5.34 cm / 2 = 2.67 cm
f = 2.67 cm / 2 = 1.335 cm
Since the image is virtual, the image distance (v) will be negative.
Substituting the values into the magnification formula:
m = - (v / u)
We can rearrange the formula to solve for the image distance:
v = - (m * u)
Plugging in the known values:
v = - (m * 10.3 cm)
Now, we can calculate the magnification using the given parameters.
To find the magnification of the image, we need to know the distance between the object and the ornament, as well as the distance between the image and the ornament. However, you have only provided the distance between the object and the ornament.
Assuming that the object is placed between the ornament and a viewer, we can calculate the approximate magnification using the formula:
Magnification = -(distance between image and ornament) / (distance between object and ornament)
Since you haven't provided the distance between the image and the ornament, it is not possible to give an accurate answer to the magnification. Please provide the additional information, or clarify the setup of the problem, so that we can provide a more precise answer.