Chapter 17, Problem 86A

To determine

To verify:The focal length of the mirror.

Explanation of Solution

Given:

Height of the object is 12 cm.

Height of the image is 2.0 cm.

Image position is 26.0 cm.

Object position is 12.0 cm.

Formula used:

The famous mirror formula can be expressed as

  $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$  ....... (1)

Here, $f,v$ and $u$ are focal length of the concave mirror, image distance and object distance respectively.

Magnification is calculated as

  $m=\frac{heightofimage}{heightofobject}$  ......(2)

Calculation:

Rearrange the equation (1) for $f$,$\frac{1}{f}=\frac{v+u}{vu}$

  $f=\frac{vu}{v+u}$  ......(2)

Substitute 12 cm for $u$ and 26 cm for $v$ in equation (2)

  $\begin{array}{l}f=\frac{26\times 12{\text{cm}}^{\text{2}}}{\left(26+12\right)\text{cm}}\\ \boxed{f=8.21\text{cm}}\end{array}$

Magnification is calculated as

  $\begin{array}{l}m=\frac{heightofimage}{heightofobject}\\ m=\frac{2\text{cm}}{12\text{cm}}\\ m=\frac{1}{6}\end{array}$