Answer to Question #126473 in Optics for Stefanie Hernandez-Mendez

Question

Consider a makeup mirror that produces a magnification of 1.3 when a person’s face is 13 cm away.
What is the focal length of the makeup mirror in meters?

Answer 1

To get focal length first we need to find the image distance which can be obtained by the magnification formula

$m =-\frac{image distance} { object distance}$

substituting the values given

$1.3=-\frac{imagedistance}{0.13}$

image distance v = -0.169 meters (The negative values imply that the image is virtual)

Now that the value of v is known, the focal length can be computed by the lens formula

$\frac{1}{f}=\frac{1}{u} +\frac{1}{v}$

substituting the values n the formula

$\frac{1}{f}=\frac{1}{0.13 }+\frac{ 1}{0.169}$

$\frac{1}{f}=\frac{2300}{169}$

$f= 0.0735m$

Answer= 0.0735m