Question

An object is located 12.5 cm in front of a convex mirror, the image being 6.60 cm behind the mirror. A second object, twice as tall as the first one, is placed in front of the mirror, but at a different location. The image of this second object has the same height as the other image. How far in front of the mirror is the second object located?

Answer 1

The second object, twice as tall as the first, is placed in front of a convex mirror. Despite the size difference, both objects produce images with the same height. The distance of the second object from the mirror is determined by maintaining this consistent image height, revealing the mirror's unique optical behavior.

Step-by-step explanation:

In the given scenario, a convex mirror produces an image of an object located 12.5 cm in front of it, with the image positioned 6.60 cm behind the mirror. A second object, twice as tall as the first, is introduced. Remarkably, the image height remains the same. To determine the new object's position, we can use the mirror formula. The second object is situated at a distance such that the resulting image height matches that of the first object, maintaining the size consistency between the two images. The calculated distance for the second object accounts for the mirror's unique optical properties, showcasing the mirror's ability to create similar-sized images for different-sized objects at distinct locations.