A 1-cm-long horse fly hovers 2.0 cm from a shiny sphere with a radius of 30.0 cm

Question

A 1-cm-long horse fly hovers 2.0 cm from a shiny sphere with a radius of 30.0 cm. Describe the location of the image of the fly, its type (real or virtual), and its length. dI = __cm and hI = __cm

I know the answers are dI= -1.76 and hI= 0.882 but I dont know how.

The program says this as a hint: "A shiny sphere can be treated as a spherical convex mirror with a radius of curvature R = 30.0 cm. A horse fly (hO = 1.0 cm) is positioned at a distance dO = 2.0 cm in front of the sphere. We can use the mirror equation, 1/dO + 1/dI = 1/f , and the definition of the magnification, m = - dI/dO to calculate the image distance, magnification, and type of the image (i.e., real or virtual, inverted or upright). We'll assume the surface of the sphere is located at the origin"

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Explanation / Answer

Here,

radius of curvature ,r = -30 cm

f = -30/2 = -15 cm

object distance , do = 2 cm

height of fly ,ho = 1 cm

Using Mirror formula

1/f = 1/di +1/do

-1/15 = 1/di +1/2

di = -1.76 cm

the image is located at dl = - 1.76 cm

----------------

as m = -di/do = -hi/ho

1.76/2 = di/1

di = 0.882 cm

the height of image is 0.882 cm

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