Lenses and Images

As a light ray refracts into and out of a lens, are there certain paths that the ray consistently follows?

Shown below is a lens with a convex curve (Figure 1a-b).  What happens to a group of parallel light rays that strike the right surface of the lens?  All of these rays appear to refract and converge at a point on the left side of the lens (Figure 2).  This point is called the focal point of the lens.  Note that the incident rays are also all parallel to the optic axis of the lens.  This is the first special ray we can use to help locate images seen in a lens: (1)  Any incident ray parallel to the optic axis will refract and pass through the focal point on the opposite side of the lens.

Figure 2, Light rays enter a convex lens parallel to the axis, and leave the lens to converge on the focal point.

When an incident ray passes through the focal point, and then strikes the lens, what path does it take as it exits the lens?  See below in Figure 3.

Above you can see the second special ray we can use to locate the image of an object seen in a lens:  (2)  When an incident ray passes through the focal point and then into the lens it exits along a path that is parallel to the optic axis.

How can we use the three special rays found above to locate the position of an image seen in a lens?

Figure 3

Below three rays are shown leaving the same point on the top of Fred’s head.  These are the rays we have seen before and we can predict their paths as they exit the lens (three special rays from above).  Follow each incident ray to make sure it follows the refracted path that we observed in our class experiments and in the pictures above.

Notice that all three refracted rays meet at a common point, F, shown below.  This point is called the focus and can also be called an image point.

Notice that as Gwen looks toward the lens she sees light rays that carry information about the top of Fred’s head, and all these light rays seem to be coming from point F.  This means the image she sees of the top of Fred’s head is at point F.  Fred actually looks as though he is in front of the lens from her perspective.

Notice that if Gwen moved around she would receive different rays coming from point F, but she would still see the image of Fred at F.

When an incident ray is headed along a path directly towards the center of the lens, what path does it take as it exits the lens?

Above you can see the third special ray we can use to locate the image of an object seen in a lens:  (3)  When an incident ray is headed toward the center of the lens, it passes through with no significant deflection from its original path.  In other words the ray essentially passes straight through the lens.

Now you can predict the refracted paths of three different types of incident rays.  These three incident rays are special simply because it is easy to predict their path when they exit the lens.

F

focal point

Figure 1a, The Light-box optics set-up, with a convex lens.

Figure 3, Light rays enter a convex lens after passing through the focal point on the right.  They emerge on the left of the lens traveling parallel to the principle axis.

Figure 1b, the convex lens

copyright Marcus Milling  2009

optic axis

incident rays

refracted rays