**Examples for lenses**

Example #1

Problem:

a.) A converging lens (convex) has a focal
length of 14 *cm*. Looking through the lens, one sees an image 20 *cm*
behind the lens. Where is the object?

Solution: Since the image is behind the lens, it is virtual
and the distance * d_{i}* is negative. Using the formula, , one can solve for

* d_{o} *= 8.24

b.) If the height of the object is 1.5 *cm*,
what is the height of the image.

Solution: Using the formula, to get

* h_{i} *= 3.64

Example #2

Problem:

A real image of a coin is observed 34 *cm*
beyond a lens. The image height is 1.4 *cm* and it is known that the actual coin is
0.7 *cm* high. What is the focal length of the lens?

Solution: First, find the object distance using . Remember that since the image is real, that the image
height is negative. ( * d_{o }*=
17

_{ }f = 11.33 *cm*

Example #3

Problem:

An object is place half way between a
converging lens and it's focal point. The focal distance is 8 *cm*.

a.) Where is the image?

Solution: Use with 4*
cm *for ** d_{o}**.

** d_{i}**
= -8

b.) What is the magnification?

** m**
= 2