Answer: 10 cm
Explanation:
[tex]$The focal length is: \\ \\ \begin{aligned}f &=\frac{R}{2} \\&=-\frac{46}{2} \\f &=-20 \mathrm{~cm}\end{aligned}$[/tex]
[tex]$ Since the image is virtual: \\ \\ :\begin{aligned}\frac{v}{u} &=m \\\Rightarrow & v=m u \\\Rightarrow &v=2 u\end{aligned}$[/tex]
[tex]$ Using: \\ \\ \begin{aligned}&\frac{1}{l}=\frac{1}{v}+\frac{1}{u} \\&\frac{1}{20}=-\frac{1}{2 u}+\frac{1}{u} \\&\frac{1}{2 u}=\frac{1}{-20} \\&\Rightarrow u=-10 \\&\therefore u=10 \mathrm{~cm}\end{aligned}$[/tex]
Therefore, you must be 10 cm away from the mirror so that your virtual image is twice the size of your actual face
