Use the following formula:
[tex]\frac{1}{f}=\frac{1}{s_o}+\frac{1}{s_i}[/tex]where,
f: focal length of the mirror = 1.5 cm (positive because it is concave)
so: object distance = 3.0cm
si: image distance = ?
Solve the equation above for si:
[tex]\begin{gathered} \frac{1}{s_i}=\frac{1}{f}-\frac{1}{s_o}=\frac{s_o-f}{f\cdot s_o} \\ s_i=\frac{f\cdot s_o}{s_o-f} \end{gathered}[/tex]Then, replace the values of the given parameters and simplify:
[tex]s_i=\frac{(1.5cm)(3.0cm)}{3.0\operatorname{cm}-1.5\operatorname{cm}}=\frac{4.5\operatorname{cm}^2}{1.5\operatorname{cm}}=3.0\operatorname{cm}[/tex]Hence, the image distance is 3.0cm
