Example Problem on solving a Concave Mirror Problem

A 4.00-cm tall light bulb is placed a distance of 45.7 cm from a concave mirror having a focal length of 15.2 cm. Determine the image distance and the image size.

Like all problems in physics, begin by the identification of the known information.

h_{o} = 4.0 cm | d_{o} = 45.7 cm | f = 15.2 cm |

Next identify the unknown quantities that you wish to solve for.

To determine the image distance, the mirror equation must be used. The following lines represent the solution to the image distance; substitutions and algebraic steps are shown.

1/f = 1/do + 1/d_{i}1/(15.2 cm) = 1/(45.7 cm) + 1/d_{i}

0.0658 cm^{-1} = 0.0219 cm^{-1 }+ 1/d_{i}

0.0439 cm^{-1} = 1/d_{i}

The numerical values in the solution above were rounded when written down, yet un-rounded numbers were used in all calculations. The final answer is rounded to the third significant digit.

To determine the image height, the magnification equation is needed. Since three of the four quantities in the equation (disregarding the M) are known, the fourth quantity can be calculated. The solution is shown below.

h_{i}/h_{o} = - d_{i}/d_{o}h_{i }/(4.0 cm) = - (22.8 cm)/(45.7 cm)

h_{i }= - (4.0 cm) • (22.8 cm)/(45.7 cm)