Question

A certain Christmas tree ornament is a silver sphere having a diameter of 8.76 cm. (a) If the size of an image created by reflection in the ornament is one-fourth the reflected object's actual size, determine the object's location. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. cm in front of the sphere (b) Use a principal-ray diagram to determine whether the image is upright or inverted. upright inverted

Answer 1

To determine the object's location and whether the image is upright or inverted, we can use the lens equation and ray tracing. Given that the size of the image is one-fourth the size of the object, we can use the magnification formula. The object is located approximately 34.40 cm in front of the sphere, and the image is inverted.

Step-by-step explanation:

To determine the object's location and whether the image is upright or inverted, we can use the lens equation and ray tracing. Given that the size of the image is one-fourth the size of the object, we can use the magnification formula. Let's assume the object is located at a distance of 'd' in front of the sphere.

The magnification formula is given by: m = -di/do, where m is the magnification, di is the image distance, and do is the object distance. From the given information, we have m = 1/4, di = -8.76 cm, and do = -d. Substituting these values into the formula, we get -1/4 = -8.76/d. Solving for 'd', we find that the object is located approximately 34.40 cm in front of the sphere.

To determine whether the image is upright or inverted, we can use a principal-ray diagram. In this case, since the magnification is a negative value, the image is inverted.