For you to see the something in a mirror, light rays must travel from the object, reflect off the mirror, and enter your eye. When you look at something through an optical element, the object appears to be located at what's called the image location. When brushing your teeth, you appear to be on the other side of the mirror because you are looking at your image. In the case of a planer mirror, the distance ($d_o$) between the object and the optical element (mirror), is the same as the distance ($d_i$) between the image and the mirror. The image is also considered a virtual image, because the rays do not actually travel through the location of the image. This can visualized by tracing two rays that diverge from the object, spreading out until hitting the mirror. They then reflect off the mirror and continue to spread out until they hit your eye. If you trace the rays back past the mirror, to where they appear to have originally diverged from, you'll find location of the image. After all, if the mirror was infinite in size and perfectly polished, you'd not know that you're looking at a image. Most illusions performed by magicians are based on images fooling the eyes.

Thin Lenses

Lenses are a common optical element found in glasses, microscopes, telescopes, and many other devices. They can be used to change the location, orientation, and size of an object's image. To use ray tracing to determine information about the image in a system with a lens, the diagram is usually drawn with a long horizontal line called the optical axis. The lens, although having some thickness, is treated like a plane perpendicular to the optical axis that redirects the rays according to the set of rules below. The object is often represented as an arrow so that the upward direction is defined. The focal point ($f$) of the lens is also drawn - the focal point is equal to half the radius ($R$) of curvature of the lens ($2f=R$).

Three Special Rays

Converging Lens

1. Parallel to the optical axis and refracts through the far focal point
2. Straight line through center of optical element
3. Through the near focal point, refracts parallel to the optical axis

Here the distance to the object is $d_o$ and the distance to the image is $d_i$. For this distance from a converging lens with this focal point, the image is inverted and smaller in size. The image is considered a real image since the rays actually travel through the location of the image.

Diverging Lens

1. Parallel to the optical axis and refracts through as if came from near focal point
2. Straight line through center of optical element
3. Towards far focal point, refracts parallel to the optical axis

Here the ray diagram shows the image is smaller and upright. The image this time is virtual though since all the rays didn't not travel through that location. For diverging lenses the image is always virtual - you must trace backwards to find where the rays appear to have diverged from. In the diagram above you see that rays 1 and 3 had to be traced backward, denoted by the dotted lines. Converging lens can create virtual images if the object is within the focal point of the lens. For a summary of all the different ray diagrams see the PDF at the bottom of this introduction.

LensesPoster_0.pdf (289.59 KB)

Now, take a look at the pre-lecture reading and videos below.