# Spherical mirror radius of curvature

1. Aug 11, 2011

### roam

1. The problem statement, all variables and given/known data

A dentist uses a spherical mirror to examine a tooth. The tooth is 1.13 cm in front of the mirror, and the image is formed 10.8 cm behind the mirror. Determine the mirror's radius of curvature.

2. Relevant equations

1/p+1/q=1/f

f=R/2

3. The attempt at a solution

Since the object is in front of the mirror, p > 0. With the image behind the mirror q < 0. So the radius of curvature is

$$\frac{2}{R}=\frac{1}{p} + \frac{1}{q} = \frac{1}{1.13} - \frac{1}{10.8} = \frac{10.8-1.13}{10.8}$$

So $$R = 2 \frac{10.8}{9.67} = 2.233$$

Why is my answer is wrong? I think I used the correct equations. I tried the same question with different numbers and the computer still marks my answer wrong. Any explanation would be appreciated.

2. Aug 11, 2011

### kuruman

$\frac{1}{1.13}-\frac{1}{10.8}\neq\frac{10.8-1.13}{10.8}$

3. Aug 11, 2011

### PeterO

You mucked up the subtraction of two fractions - in particular, the denominator.