$13.1.5.$ The object is located on the main optical axis of the concave mirror at a distance of 60 cm from the mirror pole. Determine the focal length of the mirror, if the image of the subject is valid and enlarged by one and a half times.
Solution
If image is enlarged by one and a half times, $k = \frac{s'}{s}$(1) where $k$ = 1.5 is the magnification of the image, $s$ is the object-mirror distance and $s'$ is the image-mirror distance. It's known that, $\frac{1}{s}+\frac{1}{s'}=\frac{1}{f}$(2) From (1), $s' = ks$(3) Putting (3) into (2): $f = \frac{ks}{k+1} = 36\;\rm{cm}$