A 2cm tall object is placed 15cm in front of a concave mirror of focal length 10cm. What is the size and nature of the image?

$\begin{array}{l}\text{ According to New Cartesian sign convention, }\\ \text{ Object distance u}=-15 \text{cm}\\ \text{ Focal length of a concave lens, f}=-10 \text{cm}.\\ {\text{ Height of the object h}}_0=2.0 \text{cm}\\ \text{ According to mirror formula, }\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\\ \Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u}=\frac{1}{-10}-\frac{1}{-15}\\ \Rightarrow v=-30 \text{cm}\\ \text{This image is formed 30 cm from the mirror on the same side of the object. }\\ \text{It is real image.}\\ \text{ Magnification of the mirror, }m=\frac{-v}{u}=\frac{h_i}{h_0}\\ \Rightarrow \frac{-(-30)}{-15}=\frac{h_i}{2}\\ \Rightarrow h_i=-4 \text{cm}\\ \text{ Negative sign shows that image is inverted. }\\ \text{ The image is real, inverted, of size }4 \text{cm at a distance }30 \text{cm in front of the }mirror.\\ \end{array}$