Solution to Spherical Mirror Problem

 The Problem:

A small object lies 4 cm to the left of the vertex of a concave mirror who radius of curvature is 12 cm. Find the magnification of the image.  Include a basic sketch to show the relation of the image to the object position relative to the mirror.

Solution:

We apply the mirror equation: 1/s  + 1/s’ = 2 /R

Where: s = 4 cm, which is positive (to left of mirror). Also, we have R = 12 cm. Then we need to find s’ the image distance:

1/s’ =  2/ R – 1/s = 2/12 – ¼ = 1/6 – ¼ 

For which s’ = -12 cm

The negative sign denotes a virtual image which lies to the right of the mirror and this situation can be depicted as shown below:

The magnification of the image is just: M = s’/s = h’/ h

So: M =  ï s’/s ï  = ï -12cm /4 cm ï    = 4