Solution

Statement

$13.1.15.$ 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):
$f = \frac{ks}{k+1} = 36\;\rm{cm}$