Final answer:
The distance of the image from the store's security mirror is 0.48 meters.
Step-by-step explanation:
To determine the image's distance from the store's security mirror, we can use the concept of similar triangles in optics, specifically using the properties of similar triangles formed by the girl, her image, and the mirror.
The height of the girl is 1.8 meters, and her image's height is 0.36 meters. Since the girl and her image form similar triangles with the mirror, the ratio of their heights will be equal to the ratio of their distances from the mirror.
Using the ratio of heights: 1.8 meters (girl's height) / 0.36 meters (image's height) = 2.4 meters (distance from the mirror) / x (image's distance from the mirror).
Solving for x (image's distance from the mirror), x = (0.36 meters * 2.4 meters) / 1.8 meters = 0.48 meters.
Therefore, the image's distance from the store's security mirror is calculated to be 0.48 meters, applying the concept of similar triangles and proportions between the heights and distances of the girl and her image in relation to the mirror.