(a) The mirror equation which relates the focal length f, the distance of the object [tex]d_o[/tex] and the distance of the image [tex]d_i[/tex] is
[tex] \frac{1}{f}= \frac{1}{d_o} + \frac{1}{d_i} [/tex]
where for sign convention we take the focal length of a convex mirror as negative : [tex]f=-20 cm[/tex].
Since we know the distance of the object from the mirror, [tex]d_o=12 cm[/tex], we can find the distance of the image:
[tex] \frac{1}{-20}= \frac{1}{12} + \frac{1}{d_i} [/tex]
from which
[tex]d_i=-7.52 cm[/tex]
where the negative sign means the image is virtual (located behind the mirror).
(b) We can find the height of the image through the magnification (M) equation:[tex]M= \frac{h_i}{h_o}= -\frac{d_i}{d_o} [/tex]
where [tex]h_i[/tex] and [tex]h_o[/tex] are the height of the image and the object, respectively
.Using [tex]h_o=3 cm[/tex] we can find [tex]h_i[/tex]:
[tex]h_i=h_o ( \frac{-d_i}{d_o})=(3 cm)( \frac{7.52 cm}{12 cm} )=1.88 cm [/tex]
where the positive sign means the image is upright.
