**
Image Formation by a Converging Lens**

You can move the object around by either clicking and draging or
just clicking in the location of your choice.
While the image stays real it
appears on the right of the lens as a green arrow. When the image
becomes virtual, it appeares on the left of the lens as a gray
arrow. When the object is placed exactly at the focal point, the image
appears at infinity.

The above applet shows: two arrows, a converging lens, and rays of
light being emmitted by the red arrow. The **red arrow** is the
**object**, while the **green arrow** is the **image** that
results after the rays have passed through the lens. The applet also
displays two **focus** shown as blue dots.
The image formed by a converging lens can be made using only
three principal rays.

Ray 1 is the ray which travels parallel to the
axis and after going through the lens it passes through the focal
point.
Ray 2 passes through the center of the lens.
Ray 3 goes through the focal point and then travels parallel to the
axis after passing through the lens.
Thus any point on the object can be mapped,
using the rays above, into a corresponding point on the image. This
point is located on the intersection of the rays.
The above is a useful tecnique, but it usually involves a
drawing of some sort. A more practical way is not as complete but is
much simpler. You can find the distance of the image from the lens
by the following equation:

**1/d**_{i} + 1/d_{o} = 1/f ,
where **d**_{i} is the distance from the lens to the image,
**d**_{o} is the distance from the object to the lens, and
**f** is the focal distance of the lens.
Interesting things happen when **d**_{o} is equal to
or greater than **f**. When you place the object directly at the
focal point, solving the above equation for **d**_{i} we
get:

**d**_{i} = 0,
i.e., no image results at all.
As the object is moved closer toward the lens, the image distance
tends to zero from the negative side. This is called a virtual image
represented by a gray arrow in this applet. Although the rays of
light do not intersect, the mind perceives them to be coming from a
point on the other side of the lens (this is shown by the dark green
lines), which is infact the location of the virtual image.

© Copyright 1997,
Sergey Kiselev
and
Tanya Yanovsky-Kiselev

Last modified: June 20, 1997