Answer to Question #93543 in Optics for jane montgomery

Question

There is a convex spherical mirror with a focal length of 16.00 cm. When a figurine is placed in front of it, an upright image 3.00 cm tall is formed 6.80 cm behind the mirror.
Find the position of the figurine
Find the magnification of the image

Answer 1

$\frac{1}{a_1}-\frac{1}{a_2}=-\frac{1}{F}$

$a_1=\frac{Fa_2}{F-a_2}=\frac{16*6.8}{16-6.8}=11.8cm$

$k=\frac{y_2}{y_1}=\frac{a_2}{a_1}$

$k=\frac{6.8}{ 11.8}=0.58$

$y_1=\frac{3}{0.58}=5,2cm$

Answer $1) a_1=11.8cm$ $2) k=0.58$ $y_1=5.2cm$