The nature of shaving mirror is concave
Now using magnification formula
[tex]\begin{gathered} magnification=\frac{v}{u}\begin{cases}v={image\text{ distance}} \\ u={object\text{ distance}}\end{cases} \\ \end{gathered}[/tex]
Again
[tex]\begin{gathered} \frac{1}{f}=\frac{1}{u}+\frac{1}{v}; \\ \frac{1}{f}=\frac{1}{15.2}\text{ +}\frac{1}{18}; \\ \frac{1}{f}=\text{ }\frac{18+15.2}{15.2\times18}=\frac{33.2}{273.6}=\frac{332}{2736}; \\ f=\text{ }\frac{2736}{332}\text{ cm = 8.24cm} \end{gathered}[/tex]For upright image , object should be placed between principle focus and pole
Using magnification formula we get
[tex]\begin{gathered} magnification=\text{ }\frac{v}{u}; \\ \therefore2=\frac{18}{u}; \\ u=\frac{18}{2}=9\text{ cm} \end{gathered}[/tex]To satisfy both conditions object must be put at a distance less than 8.24 cm
Answer is:- face distance from mirror is less than 8.24 cm
