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 characteristics of the image formed by the reflecting spherical Christmas tree ornament, we can use the mirror equation:
1/f = 1/di + 1/do
where:
f is the focal length of the ornament,
di is the distance of the image from the ornament, and
do is the distance of the object (child) from the ornament.
Given:
Diameter of the ornament (d) = 12 cm
Distance of the child (do) = 18 cm
First, let's find the focal length of the ornament. For a spherical mirror, the focal length is half of the radius of curvature (f = R/2).
The radius of the ornament (R) can be determined by dividing the diameter by 2:
R = d/2 = 12 cm / 2 = 6 cm
Now we can calculate the focal length:
f = R/2 = 6 cm / 2 = 3 cm
Substituting the known values into the mirror equation:
1/f = 1/di + 1/do
Rearranging the equation to solve for the distance of the image (di):
1/di = 1/f - 1/do
Substituting the values:
1/di = 1/3 cm - 1/18 cm
To simplify the equation, we can find the common denominator:
1/di = (6 - 1)/18 cm = 5/18 cm
Taking the reciprocal of both sides to solve for di:
di = 18/5 cm = 3.6 cm
Therefore, the image will form at a distance of 3.6 cm from the ornament.