A mirror is created by spraying the outside of a large sphere with silver paint

Question

A mirror is created by spraying the outside of a large sphere with silver paint which reflects light with high efficiency. The ball has a diameter of 5.2 meters. An object is placed a distance of 1.9 m from the surface of the sphere. The object as a height of 3 cm.

1. What is the focal length of this mirror? (f = ?)

For this question, I got 1.3 as the focal length, but my answer was apparently wrong. I took the radius of 2.6 / 2 to find 1.3.

2. How far from the surface is the image, counting positive distances in front of the mirror? (d = ?)

3. What is the magnification of the image? (M = ?)

4. What is the height of the image? (H = ?)

.

Explanation / Answer

R = d/2 = 2.6m

f = R/2 = -1.3m ( convex mirror)

part 2 )

1/do + 1/di = 1/f

1/di = 1/f - 1/do

do = 1.9 m

1di = -0.772 m

part 3 )

m = -di/do

m = 0.40625

part 4 )

m = hi/ho

hi = m*ho

hi = 1.21875 cm

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