Chapter 23, Problem 102A

To determine

Location of object image.

Answer to Problem 102A

Location of image will be 13.37 cm back side of mirror.

Explanation of Solution

Given:

Object distance from mirror, $u=12.6\text{ cm}$

Focal length, $f=218\text{ cm}$

Formula used:

The focal length f is,

  $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

Where, u is object distance and vis image distance.

Calculation:

Substituting the value of u and f and solve.

  $\begin{array}{c}\frac{1}{218}=\frac{1}{12.6}+\frac{1}{v}\\ \frac{1}{v}=\frac{1}{128}-\frac{1}{12.6}\\ \frac{1}{v}=0.00458-0.0793\\ \frac{1}{v}=-0.0747\\ v=-13.37\text{ cm}\end{array}$

Conclusion:

Therefore, image will form at a distance of 13.37 cm from mirror here negative sign indicates that image will form back side of mirror.