Final answer:
The image distance for an object placed in front of a convex mirror is calculated using the mirror equation. The image distance found is approximately -2.18 cm, indicating a virtual image behind the mirror.
Step-by-step explanation:
The question involves finding the image distance of an object placed in front of a convex mirror using the mirror equation. The mirror equation for a convex mirror is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. Since the convex mirror has a focal length of 8 cm, and the object distance (do) is 3 cm, we plug these into the equation. Remember that for a convex mirror, the focal length is taken as negative (-8 cm in this case). So, the equation becomes:
1/(-8) = 1/3 + 1/di
This gives us:
-1/8 = 1/3 + 1/di
Bringing 1/3 to the left side, we get:
-1/8 - 1/3 = 1/di
Finding a common denominator, we have:
-3/24 - 8/24 = 1/di
-11/24 = 1/di
Therefore, di = -24/11 cm, which is approximately -2.18 cm.
Since the image distance is negative, this indicates that the image is virtual and is located behind the mirror.