Answer
$-100\;\rm cm$
Work Step by Step
We know that the magnification of the given mirror is given by
$$m=\dfrac{h'}{h}=\dfrac{-s'}{s}$$
Hence,
$$m=\dfrac{1}{2}=\dfrac{-s'}{s}$$
Thus,
$$s=-2s'\tag 1$$
which means that the distance between the
where the distance between the object and the image is 150 cm, so $s'+s=150$ cm. So that $s'+2s'=150$.
Thus,
$$s'=\bf -50\;\rm cm\tag 2$$
The negative sign is due to the virtual image since it is upright and is formed behind the mirror.
and hence,
$$s=\bf 100\;\rm cm$$
Now we can find the focal length by using the thin lens formula,
$$\dfrac{1}{s}+\dfrac{1}{s'}=\dfrac{1}{f}$$
Hence,
$$f=\left[ \dfrac{1}{s}+\dfrac{1}{s'}\right]^{-1}$$
Plugging from (1),
$$f=\left[ \dfrac{1}{-2s'}+\dfrac{1}{s'}\right]^{-1}$$
Plugging from (2),
$$f=\left[ \dfrac{1}{-2(-50)}+\dfrac{1}{(-50)}\right]^{-1}$$
$$f=\color{red}{\bf-100}\;\rm cm$$
Since the focal length is negative, it must be a convex mirror.
