Chapter 17.2, Problem 14PP

To determine

The image position.

Answer to Problem 14PP

  $28.8\text{cm}$

Explanation of Solution

Given:

The focal length of the concave mirror, $f=16.0\text{cm}$

The object distance from the mirror, $d_o=36.0\text{cm}$

Formula used:

Mirror equation,

  $\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}$

Where,

  $\begin{array}{l}f=\text{focal length}\\ d_i=\text{ image distance}\\ d_o=\text{object distance}\end{array}$

Calculation:

Using the given values in Mirror equation, the image distance will be,

  $\begin{array}{c}\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}\\ \frac{1}{16}=\frac{1}{d_i}+\frac{1}{36}\\ d_i=\frac{36\times 16}{36-16}\\ =28.8\text{cm}\end{array}$

Conclusion:

Hence, the image is formed at a distance of $28.8\text{cm}$ from the mirror.