PHYS 2212 Module 14.4

Thin Lenses

Learning Objectives

By the end of this section, you will be able to:

• Use ray diagrams to locate and describe the image formed by a lens
• Employ the thin-lens equation to describe and locate the image formed by a lens

Ray Diagrams

Here are the steps to drawing ray diagrams:

1. Draw the lens (a side view like I’ve been doing) and a long, horizontal line through the center. This line is called the central axis, or the optical axis.
2. Draw both focal points of the lens (remember they are symmetric, so the distance f will be the same on both sides). Just draw them as dots.
3. Then draw the object at the appropriate distance from the lens (d_o). We usually draw the object as a vertical arrow pointing upward. This is to allow us to figure out if the image will be inverted (upside down) or not. An arrow has a definite top and bottom to it, so it makes it easy.
4. Draw exactly 3 special rays, and trace them through the lens. These special rays are called principle light rays and they follow very specific paths. Each ray starts at the top of the object.
   1. Draw a ray that starts at the top of the object and runs parallel to the optical axis. When this light ray gets to the lens, it will bend inward and go through the focal point. 
   2. Draw a ray that starts at the top of the object and goes through the center of the lens. This will continue in a straight line through the lens and won’t bend.
   3. Draw a ray that starts at the top of the object and goes through the focal point on the object-side of the lens. When this reaches the lens, it will bend so that it exits the lens parallel to the optical axis. (Remember how lenses are symmetrical.)
5. Where the three principle light rays converge is where the image forms. Since the rays started at the top of the object, you will see an image of the top of the object at the point where the light rays converge.

Converging (Convex) Lenses

Diverging Lenses

The Lens Equation and Magnification

The equations we use for spherical lenses are the same as those for spherical mirrors. The lens equation is

and the lateral magnification is

Sign Conventions

We have to be careful about the signs (+ or -) that we use when we describe the distances and the magnification. Here is a table to help with the signs:

	Converging (Convex) Lens	Diverging (Concave) Lens
Real Object	+ do	+ do
Real Image	+ di	N/A (concave lenses cannot form real images)
Virtual Image	– di	– di
Focal Length	+ f	– f

The power of the corrective lenses is equal to the inverse of the focal length measured in meters. Use the thin lens equation to determine the inverse of the focal length, or the power of the corrective lenses:

making sure to use object and image distances that are measured from the corrective lens and not the eye’s lens.