Chapter 17, Problem 78A

To determine

The image distance from the mirror.

Answer to Problem 78A

At a distance of $6.94\text{cm}$ image is formed behind the mirror.

Explanation of Solution

Given:

The radius of curvature of the concave mirror, $R=24.0\text{cm}$

The object distance from the mirror, $d_o=4.4\text{cm}$

Formula used:

The relation between the radius of curvature of mirror $\left(R\right)$ and its focal length $\left(f\right)$ is,

  $f=\frac{R}{2}$

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:

Then, the focal length of the concave mirror will be,

  $f=\frac{R}{2}=\frac{24.0\text{}\text{cm}}{2}=12.0\text{}\text{cm}$

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

  $\begin{array}{c}\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}\\ \frac{1}{12}=\frac{1}{d_i}+\frac{1}{4.4}\\ d_i=\frac{4.4\times 12}{4.4-12}\\ =-6.94\text{cm}\end{array}$

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

Conclusion:

Therefore, the image is located at a distance of $6.94\text{cm}$ behind the mirror.