Chapter 18, Problem 93A

To determine

The focal length of the lens.

Answer to Problem 93A

  $6.67\text{cm}$

Explanation of Solution

Given:

The object distance from the lens, $d_o=20\text{cm}$

The image distance from the lens, $d_i=10\text{cm}$ (it will be positive since real image is formed)

Formula used:

Thin lens equation,

  $\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}$

Where,

  $\begin{array}{l}f=\text{focal length of the lens}\\ d_i=\text{ image distance}\\ d_o=\text{object distance}\end{array}$

Calculation:

Using the given values in Thin lens equation, the focal length will be,

  $\begin{array}{c}\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}\\ \frac{1}{f}=\frac{1}{10}+\frac{1}{20}\\ f=\frac{20\times 10}{20+10}\\ =6.67\text{cm}\end{array}$

Conclusion:

Hence, focal length of the lens is $6.67\text{cm}$ .