$$
begin{align*}
f = -frac{1}{2}R
end{align*}
$$

While the focal length for a concave mirror of radius $R$ is given by

$$
begin{align*}
f = frac{1}{2}R
end{align*}
$$

We plug in the value $R = 0.86;text{m}$ for the convex mirror focal length equation.

$$
begin{align*}
f = -frac{1}{2}(0.86;text{m}) = boxed{-0.43;text{m}}
end{align*}
$$

We plug in the value $R = 0.86;text{m}$ for the concave mirror focal length equation.

$$
begin{align*}
f = frac{1}{2}(0.86;text{m}) = boxed{0.43;text{m}}
end{align*}
$$

(b) $f = 0.43$ m

Hence the radius curvature is $R=2f=2times (15 {rm cm})=30$ cm

The mirror is concave $Rightarrow f>0$

$d_o>fRightarrow$ The image is real $Rightarrow d_i>0$

$frac{1}{d_i}=frac{1}{f}-frac{1}{d_o}=frac{d_o-f}{d_of}Rightarrow d_i=frac{d_of}{d_o-f}=frac{2*0.5}{2-0.5}=boxed{0.67m}$

The magnification equation states:

$$
m=-frac{d_i}{d_o}=boxed{-0.33}
$$

$$
m=frac{h_i}{h_o}Rightarrow h_i=m*h_o=(-0.33)*42=boxed{14cm}
$$