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 foci shown as blue dots.
The image formed by a converging lens can be made using only three principal rays.
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.
- 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.
The above is a useful technique, 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/di + 1/do
= 1/f , where
Interesting things happen when do is equal to or greater than
f. When you place the object directly at the focal point, solving the above
equation for di we get: di = 0, i.e., no image
results at all.
- di is the distance from the lens to the image
- do is the distance from the object to the lens
- f is the focal distance of the lens
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