Q13) An object placed 20 cm …

Distance of the object ' u '=-20 cm
Image is formed in front of the mirror at a distance (v) of -15 cm
Therefore, the focal length of the mirror ' f ' is

{tex}\begin{aligned} & \Rightarrow \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \\ & \Rightarrow \frac{1}{f}=\frac{1}{-15}+\frac{1}{-20} \\ & \Rightarrow \frac{1}{f}=-\frac{4}{60}-\frac{3}{60}=\frac{-7}{60} \\ & \Rightarrow f=\frac{-60}{7} \mathrm{~cm} \end{aligned}{/tex}

Thus, the mirror is concave and has a focal length of 60 / 7.
(ii) Distance of the object ' u ' =-20cm
Image is formed behind the mirror at a distance (v) of 15 cm
Then, the focal length of the mirror ' f ' will be
{tex}\begin{aligned} & \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \\ & \Rightarrow \frac{1}{f}=\frac{1}{15}+\frac{1}{-20} \\ & \Rightarrow \frac{1}{f}=\frac{4}{60}-\frac{3}{60}=\frac{1}{60} \end{aligned}{/tex}

f=60 
Thus, the mirror is convex and has a focal length of 60 cm.