A reflecting, spherical Christmas tree ornament has a diameter of 8.0 cm. A child looks at the ornament from a distance of 20 cm. Describe the image she sees.
image location in centimeters.
Please identify the School Subject first so we can all identify it.
Sra
32
To describe the image that the child sees in the reflecting, spherical Christmas tree ornament, we can use the principles of reflection and the properties of spherical mirrors.
1. Locate the center and radius of the ornament:
The ornament is spherical, so the center of the ornament is at its geometric center. The radius of the ornament is half of its diameter, which is 8.0 cm / 2 = 4.0 cm.
2. Determine the focal point:
A spherical mirror has a focal point, which is located at a distance of half the radius from the mirror's center. In this case, the focal point is at a distance of 4.0 cm / 2 = 2.0 cm from the center of the ornament.
3. Find the child's location:
The child is positioned at a distance of 20 cm from the ornament. This distance is measured from the center of the ornament.
4. Determine the path of light rays:
When light rays from the child's eyes reach the ornament's surface, they reflect off the surface of the ornament.
- For any incident ray passing through the focal point, the reflected ray will be parallel to the principal axis.
- For any incident ray that is parallel to the principal axis, the reflected ray will pass through the focal point.
5. Locate the image:
Using the above information, we can determine that the child's eyes will send parallel rays of light to the ornament. These light rays will hit the surface of the ornament and reflect back towards the focal point.
Since the incident rays from the child's eyes are parallel, the reflected rays will pass through the focal point. Therefore, the child will see an inverted image of the ornament located at the focal point, which is 2.0 cm away from the center of the ornament.