# A lady applies makeup, using a concave mirror, with a focal length of 10cm. At a distance of 6cm...

## Question:

A lady applies makeup, using a concave mirror, with a focal length of 10cm. At a distance of 6cm from the mirror, how large does her 4cm-wide eye appear? Solve mathematically.

## Concave Mirrors

Concave mirrors are converging mirrors. The object and image distances are measured from the mirror. If they are located in front of the mirror, the distances are positive. If they are located behind the mirror, the distances are negative. We can use the following equations to determine the missing quantities in a mirror problem:

{eq}\frac{1}{s_o}+\frac{1}{s_i}=\frac{1}{f}\\ M=-\frac{s_i}{s_o}=\frac{h_i}{h_o} {/eq}

We will use our knowledge of concave mirrors to solve this problem.

Givens:

{eq}f=10 \ cm\\ s_o=6 \ cm\\ h_o= 4 \ cm\\ {/eq}

We want to find the image height. We will need to use the following equations:

{eq}\frac{1}{s_o}+\frac{1}{s_i}=\frac{1}{f}\\ -\frac{s_i}{s_o}=\frac{h_i}{h_o} {/eq}

First, we must find the image distance:

{eq}\frac{1}{s_o}+\frac{1}{s_i}=\frac{1}{f}\\ \frac{1}{6 \ cm}+\frac{1}{s_i}=\frac{1}{10 \ cm}\\ s_i=-15 \ cm {/eq}

Next to find the height of the image:

{eq}-\frac{s_i}{s_o}=\frac{h_i}{h_o}\\ -\frac{-15 \ cm}{6 \ cm}=\frac{h_i}{4 \ cm}\\ h_i=10 \ cm {/eq}