**Examples
for lenses**

Example #1

Problem:

a.) A converging
lens (concave) 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}.

**d**_{o}_{ }= 8.24 *cm*

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 *cm***,
**upright

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 *cm *). One can then use to find the focal length.

**d**_{o}_{ }= 11.33 *cm*