Presentation: lenses

Look at these images. Just look at them. Reach for them, and touch them if you can. (These are actually real and virtual images produced by a spherical mirror at the Reuben H. Fleet Science Center, San Diego, CA.) (Video link: "080724-1040074.")

Although mirrors create images as well, we will instead focus our attention on images created by lenses.

Whereas mirrors create images by reflecting light off of their surfaces, lenses create images by refracting light through their front and rear surfaces. As a result of shaping these surfaces, two different types of lenses can be made.

First, properties of these two different types of lenses.

A converging lens will take parallel rays of light (here, from the sun) and bring them to a focus at a point in space.

A diverging lens will take parallel rays of light and "defocus" them (spread outwards) away from a point in space.

The focal point of a lens is the location in space where parallel light is brought to a focus (for a converging lens), or the location in space where parallel light is made to spread outwards from (for a diverging lens).

Second, developing a graphical model of how these lenses generate images.

Although a converging lens is a physical object with curved surfaces, our model assumes that thickness of the lens is unimportant, so we merely indicate its convex surfaces with curved top and bottom bars.

We are going to draw three principal rays for this converging lens that start from an object placed to the left of the lens (convention is that light will travel from left-to-right across these ray tracing diagrams). There are many other light rays that can be drawn, but these three principal rays should suffice to locate the image (if any) generated by this lens. (Ideally you would only need to draw two rays to locate the image at their intersection (if any), but we'll draw a third principle ray as a redundant check.)

The principal rays for a converging lens all start from the top of the object.

1. Ray travels horizontally, and the converging lens will redirect this ray through its focal point on the right.
2. Ray travels straight through the center of the lens, and continue onwards.
3. Ray travels through the focal point on the left, and the converging lens will redirect this ray horizontally.

We will practice drawing these converging lens ray diagrams for different object distances, and locate the subsequent images generated by the intersection of these principal rays on a worksheet in class. There will be subtleties not covered in these principal ray rules, but the worksheet will handle all of these special cases.

Note the symbol used here for a diverging lens--again, the thickness of the lens is unimportant, so we merely indicate its concave surfaces with curved top and bottom bars.

The principal rays for a diverging lens all start from the top of the object.

1. Ray travels horizontally, and the diverging lens will redirect this ray out away from its focal point on the left. Draw a dashed line that traces back to the focal point, indicating that for an observer on the right of the lens, the redirected ray appears to have come from the focal point on the left.
2. Ray travels straight through the center of the lens, and continue onwards.
3. Ray travels towards the focal point on the right, and the diverging lens will redirect this ray horizontally. Draw a dashed line that traces back horizontally, indicating that for an observer on the right of the lens, the redirected ray appears to have always traveled horizontally.

Again, we will practice drawing diverging lens ray tracings for different object distances, and locate the subsequent images generated by the intersection of these principal rays on a worksheet in class.

Third, the two different types of images that can be generated. These will be demonstrated by mirrors, but images generated by lenses will have the same certain attributes.

(Video link: "REFLECTIONS: Giant Spherical Mirror Tricks.") If the redirected rays of light actually intersect at a location in space, then a real image is generated. At certain viewing angles, the real image amy literally seem "float" in space at this location, and a screen can be placed at this location to show that the light rays actually intersect there.

(Video link: "Milo's Mirror.") If the redirected rays of light do not actually intersect at a location in space, but merely move outwards from an extrapolated location (here, behind the mirror), then a virtual image is generated. At certain viewing angles, the virtual image seem to be located at a point in space, but a screen cannot physically be placed at this location (which would here be behind the mirror) to show that the light rays actually intersect there.

Again, these distinguishing properties of real and virtual images are here demonstrated by mirrors, but real and virtual images generated by lenses have these same properties. These will become more apparent after completing the ray tracing worksheets below, more quantitative discussion of lenses in a subsequent presentation, and experiencing these images hands-on in open-ended labs.

This worksheet (consisting of five converging lens and five diverging lens ray tracings) will illustrate all the possible unique ray tracings for converging and diverging lenses. Neatness counts, so this is also a test of your drafting skills. You should be able to draw any and all of these ray tracings to scale for your homework, and on the quiz as well.

After completing each of these ray tracings, indicate whether the resulting image (if any) is upright or inverted (with respect to the original object), enlarged or diminished (with respect to the original object), and is real or virtual (located at an actual intersection of principal rays, or located at a backwards-extrapolated intersection of principal rays). Refer to this worksheet when we look at real-world examples of these images in a picto-quiz.

For reference, solutions to the worksheet are shown below. For the purposes of the quiz, make sure you would be able draw any and all of these ray tracings without referring to the solutions.