Chapter 23, Problem 56P

To determine

How far from a converging lens with a focal length of 32 cm should an object be placed to produce a real image which is of the same size of the object.

Answer to Problem 56P

Solution:

The object distance from the lens should be 64 cm.

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.

Magnification, $m=\left|\frac{v}{u}\right|$

Calculation:

For a positive lens real image formation requires v and u to be of opposite sign.

Thus,

$\frac{v}{u}=-1$

Using lens equation,

$-\frac{1}{u}-\frac{1}{u}=\frac{1}{32}$

This gives, $u=-\text{64 cm}$