Answer to Question #108492 in Optics for Chloe

Question

Ms. Everything is 5.13 ft tall. When standing in front of a convex mirror, her image’s height appears to be 3.18 ft. If the focal length of the mirror is 4.5 ft., what is her distance from the mirror? How far is her image from the surface of the mirror?

Answer 1

$f=\frac{R}{2}$

$\frac{1}{d_o}-\frac{1}{d_i}=-\frac{1}{f}$ and $y_i=y_o\frac{d_i}{d_o}\to$

$d_o=f(\frac{d_o}{d_i}-1)=4.5(\frac{5.13}{3.18}-1)=2.76ft$ to the left

$\frac{1}{2.76}-\frac{1}{d_i}=-\frac{1}{4.5}$ $\to$ $d_i=1.71ft$ to the right