Chapter 23, Problem 54P

To determine

(a) To determine:

How far from a 50 mm focal length lens must be placed if its image is to be magnified 2.5 times and be real

Answer to Problem 54P

Solution:

The object should be placed 70 mm before the 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.

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

Calculation:

For the image to be real v and u should have opposite sign. Thus,

$\frac{v}{u}=-2.5$

Putting this in the lens equation we get,

$\frac{1}{-2.5u}-\frac{1}{u}=\frac{1}{f}=\frac{1}{50}$

This gives, u= -70 mm.

To determine

(b) To determine:

What if the image is to virtual and magnified

Answer to Problem 54P

Solution:

The object should be placed 30 mm before the lens

Explanation of Solution

Calculation:

For image to be virtual v and u should be of the same sign.

$\frac{v}{u}=2.5$

Putting this in the lens equation,

$\frac{1}{2.5u}-\frac{1}{u}=\frac{1}{50}$

This gives, $u=-30mm$