A reflecting spherical Christmas tree ornament has a diameter of 12 cm. A child looks at the ornament from a distance of 18cm. A ... image will form at ... from the ornament

To determine the size and distance of the image formed by the reflecting spherical Christmas tree ornament, we can use the mirror formula:

1/f = 1/u + 1/v

Where:
f is the focal length of the mirror,
u is the object distance, and
v is the image distance.

In this case, the ornament is acting as a concave mirror, and the child is looking at it from a distance of 18 cm. Let's assume that the focal length of the mirror is positive for a concave mirror.

Since the object distance (u) is positive, the image distance (v) will also be positive for a real image formed by a concave mirror.

Now let's solve the problem step by step.

1. Find the focal length (f):
The focal length of a spherical mirror is given by f = R/2, where R is the radius of curvature.
Since the ornament is a sphere, the radius of curvature is half the diameter: R = 12 cm / 2 = 6 cm.
Therefore, the focal length of the mirror is f = 6 cm / 2 = 3 cm.

2. Calculate the image distance (v):
Using the mirror formula, we substitute the known values:
1/3 = 1/18 + 1/v
Simplifying the equation, we get:
1/v = 1/3 - 1/18
1/v = (6 - 1)/18 = 5/18
v = 18/5 = 3.6 cm

So, the image formed by the reflecting Christmas tree ornament will be located at a distance of 3.6 cm from the ornament.

Additionally, since the ornament is a reflecting spherical mirror, the image will be inverted.