Question

An object is 25.0 cm from the center of a spherical silvered-glass Christmas tree ornament 6.20 cm in diameter. What is the position of its image (counting from the ornament surface)? Follow the sign rules. Express your answer with the appropriate units. What is the magnification of its image?

Answer 1

The position of the image is 26.8 cm from the ornament surface and the magnification is -0.915.

Step-by-step explanation:

To determine the position of the image and the magnification of an object located 25.0 cm from the center of a spherical silvered-glass Christmas tree ornament with a diameter of 6.20 cm, we can use the lens equation and magnification formula for spherical mirrors.

1. To find the position of the image, we can use the lens equation: 1/f = 1/do + 1/di. Since the object is located 25.0 cm from the center of the ornament, the object distance (do) is -25.0 cm (negative sign indicates it is on the same side as the object). The radius of the mirror is half the diameter of the ornament, giving a radius of 3.10 cm. Plugging these values into the lens equation: 1/3.10 = 1/-25.0 + 1/di, we can solve for the image distance (di).
2. To find the magnification of the image, we can use the magnification formula: m = -di/do. Using the values we previously obtained, we can calculate the magnification.

After solving the equations, the position of the image is determined to be 26.8 cm from the ornament surface (counting from the ornament surface towards the object) and the magnification of the image is -0.915.

Answer 2

The position of the image of the object on the spherical silvered-glass Christmas tree ornament is 25.83 cm in front of the ornament's surface. The magnification of the image is -1.033, indicating that the image is inverted compared to the object.

Step-by-step explanation:

To find the position of the image of an object placed in front of a spherical silvered-glass ornament, we can use the mirror equation: 1/f = 1/do + 1/di

In this case, the ornament acts as a concave mirror and the object is placed 25.0 cm from its center. The diameter of the ornament is 6.20 cm, so its radius of curvature (R) is half the diameter, which is 3.10 cm. The focal length (f) of the mirror is equal to half the radius of curvature. Therefore, f = R/2 = 1.55 cm.

Plugging in the values into the mirror equation: 1/1.55 = 1/25 + 1/di. Solving for di, we get di = 25.83 cm. Since the object is placed in front of the mirror, the image is formed on the same side as the object. Therefore, the position of the image is 25.83 cm in front of the ornament's surface.

The magnification (m) of the image can be calculated using the magnification formula: m = -di/do. In this case, di = 25.83 cm and do = 25.0 cm. Plugging in the values, we get m = -1.033. The negative sign indicates that the image is inverted compared to the object.