Chapter 23, Problem 61P

A diverging lens with f= -36.5 cm is placed 14.0 cm behind a converging lens with 20.0 cm.Where will an object at infinity be focused?

To determine

Where an object at infinity will be focused

Answer to Problem 61P

Solution:

The object will be focused 33.12 cm after the converging lens.

Explanation of Solution

Formula used:

Lens equation, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

f, u and v are lens to focal, lens to object and lens to image distances repectively, negative when opposite to optical path and positive when in the direction of optical path.

Calculation:

As the object is at infinity a virtual image of the same will be created by the diverging lens at its focal point i.e. 36.5 cm before it.

That will act as the object for the converging lens.

Thus, object distance for the converging lens is

$u=-\left(\text{36}.\text{5}+\text{14}\right)=-\text{5}0.\text{5 cm}$

Using les equation,

$\frac{1}{v}+\frac{1}{50.5}=\frac{1}{f}=\frac{1}{20}$

This gives, $v=\text{33}.\text{12 cm}$