Final answer:
Using the magnification and object distance, the image distance for a shopper's reflection in a convex security mirror is determined to be -0.68625 meters, signifying that the image is virtual and appears behind the mirror.
Step-by-step explanation:
The question concerns the image distance in a convex mirror scenario in Physics. Here, a shopper stands at a distance of 2.25 meters from a convex security mirror and observes an image magnification of 0.305. To find the image distance, measured from the surface of the mirror, we use the mirror equation and the magnification formula. The mirror equation relates object distance (do), image distance (di), and the focal length (f) of the mirror:
\(\frac{1}{do} + \frac{1}{di} = \frac{1}{f}\).
Magnification (m) is also related to the object and image distance as:
\(m = -\frac{di}{do}\).
Since the magnification is given as 0.305, we can express the image distance as a fraction of the object distance:
\(0.305 = -\frac{di}{2.25}\).
By solving the equation, we get:
\(di = -2.25 \times 0.305\).
\(di = -0.68625\) meters, which means the image appears to be 0.68625 meters behind the mirror, indicating it's a virtual image as expected for a convex mirror. Note that the negative sign indicates the image is virtual and located behind the mirror which is typical for convex mirrors.