Chapter 17, Problem 7STP

To determine

To Choose: The correct option.

Answer to Problem 7STP

D. $42\text{cm}$

Explanation of Solution

Given:

The focal length of the concave mirror, $f=14.0\text{cm}$

The object distance from the mirror, $d_o=21.0\text{cm}$

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,

  $\begin{array}{c}\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}\\ \frac{1}{14}=\frac{1}{d_i}+\frac{1}{21}\\ d_i=\frac{21\times 14}{21-14}\\ =42\text{cm}\end{array}$

Conclusion:

Hence, the image distance is $42\text{cm}$ in front of the mirror.