Chapter 17, Problem 57A

To determine

The image distance behind a convex mirror.

Answer to Problem 57A

7.23 m behind the mirror

Explanation of Solution

Given:

The focal length of the convex mirror, $f=-26.0\text{m}$

The object distance from the mirror, $d_o=10.0\text{m}$

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,

  $\begin{array}{c}\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}\\ \frac{1}{-26}=\frac{1}{d_i}+\frac{1}{10}\\ d_i=-\left(\frac{10\times 26}{10+26}\right)\\ =-7.23\text{m}\end{array}$

Negative sign denotes that the image is formed behind the mirror.

Conclusion:

Therefore, the image is formed at a distance of $7.23\text{}\text{m}$ behind the mirror.