Answer:
A. The mirror is a convex mirror
B. The radius of curvature of the convex mirror is -45.8 cm
Step-by-step explanation:
A. Obtaining the focal length
The radius of curvature is twice the size of the focal length, the focal length is related to object and image distance with the expression below;
1 / f = 1 / v + 1 / u ...................1
f is the focal length
Since the image (v) is formed at the back of the mirror v = -22.9 cm
u is the distance of the object from the mirror = ∞
Substituting into equation 1
1 / f = 1 / [(-22.9) + 1 / ∞]
1/f = 1/(-22.9)
f = -22.9
Since the focal length is negative, the mirror is convex.
B The radius of curvature
The radius of curvature is twice the focal length of the mirror and expressed thus;
radius of curvature = 2 x focal length
r = 2 x f
r = 2 x (-22.9 cm)
= -45.8 cm
Therefore the radius of curvature of the convex mirror is -45.8 cm