Final answer:
To calculate the image distance for an object in front of a convex mirror, we use the focal length (half the radius of curvature) in the mirror equation. For a radius of curvature of 12 cm, the focal length is 6 cm, leading to an image distance of 12 cm, indicating a virtual image.
Step-by-step explanation:
To determine the image distance for an object placed in front of a convex mirror using the mirror equation, we first need the focal length of the convex mirror. Since the radius of curvature (R) of the mirror is given as 12 cm, we can use the relationship f = R/2 to find the focal length (f). Therefore, f = 12 cm / 2 = 6 cm. However, for a convex mirror, the focal length is considered positive, thus f = +6 cm.
Using the mirror equation 1/f = 1/do + 1/di, where do is the object distance and di is the image distance, we can plug in the values we have. The object distance is negative for a real object in a convex mirror, so do = -12 cm. Substituting the known values we get:
1/f = -1/do + 1/di1/6 cm = -1/(-12 cm) + 1/di1/6 cm = 1/12 cm + 1/di1/di = 1/6 cm - 1/12 cm1/di = 2/12 cm - 1/12 cm1/di = 1/12 cmdi = 12 cm
The image distance (di) is thus positive 12 cm, indicating the image is virtual and located on the same side of the mirror as the object (since it's a convex mirror).