To determine the position and magnification of the image formed by a convex mirror, we can utilize the mirror equation and magnification formula.
a) The mirror equation is given as:
1/f = 1/di + 1/do
where f is the focal length, di is the image distance, and do is the object distance.
We are given the focal length (f = 52.6 cm) and the image distance (di = -20.6 cm) since the image is formed on the opposite side of the mirror. To find the object distance (do), we rearrange the equation:
1/do = 1/f - 1/di
Substituting the given values:
1/do = 1/52.6 - 1/(-20.6)
Simplifying:
1/do = 0.019 - (-0.049)
1/do = 0.068
do = 1 / 0.068
do ≈ 14.7 cm
Therefore, the crayon is positioned approximately 14.7 cm in front of the convex mirror.
b) The magnification (m) can be calculated using the formula:
m = - di / do
Substituting the given values:
m = - (-20.6) / 14.7
m = 1.4
Thus, the magnification of the image is 1.4.