Question

A dentist uses a concave mirror of radius of curvature 3 cm, and places an object at a distance of x cm from the mirror to get a magnification of +5. What is the value of x.

Answer 1

Since magnification is +5, v = 5x and u = -x. This tells us that the image is formed behind the mirror and focal length is positive.Now using mirror formula:
$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\Rightarrow \frac{1}{1.5}=\frac{1}{-x}+\frac{1}{5x}\Rightarrow \frac{1}{1.5}=\frac{-5+1}{5x}\Rightarrow \frac{1}{1.5}=\frac{-4}{5x}\Rightarrow x=\frac{-4\times 1.5}{5}=-1.2cm$
Which gives the value of x