Explanation

(a) According to new cartesian sign convention,
Object distance $u\ = \ - 40\ cm$
[image:9_image117.emf]
Image distance $\ v = \ ?$
Focal length $f = \ - 20\ cm$
$\therefore$ From mirror formula
$\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
Or $\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$
Or $\frac{1}{v} = \frac{1}{- 20} - \frac{1}{( - 40)} = \ - \frac{1}{40}$
Or $v\ = \ - 40\ cm$
$\therefore$ The image is on the same side of the object.
Now, magnification $m = \frac{v}{u} = \ - \ \frac{( - 40)}{( - 20)} = \ - 2$
Hence, the image is real, inverted and of same sie.