Chapter 17, Problem 61A

To determine

A physics problem for which the equation $\frac{1}{0.4\text{m}}=\frac{1}{0.75\text{m}}+\frac{1}{x_0}$ would be part of the solution.

Answer to Problem 61A

The question for the could be, “A convex lens is having a focal length of 0.75 m. Find the object position, if the image is formed 0.4 m behind the mirror.”

Explanation of Solution

Introduction:

The lens formula is given as,

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

Where, $f$ is focal length, $v$ is image distance and $u$ is object distance.

The question for the given equation could be, “A convex lens is having a focal length of 0.75 m. Find the object position, if the image is formed 0.4 m behind the mirror.”

And the solution is,

  $\begin{array}{l}\frac{1}{f}=\frac{1}{x_i}+\frac{1}{x_0}\\ \Rightarrow \frac{1}{0.75\text{m}}=\frac{1}{0.4\text{m}}+\frac{1}{-x_0}\\ \Rightarrow \frac{1}{x_0}=\frac{1}{0.4}-\frac{1}{0.75}=1.167\\ \Rightarrow x_0=0.86\text{m}\end{array}$

i.e. object is placed 0.86 m in front of mirror

Therefore, the question for the given equation could be, “A convex lens is having a focal length of 0.75 m. Find the object position, if the image is formed 0.4 m behind the mirror.”