\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Ray Tracing

While the lens equation can help us pin down the location and size of the image precisely, we can get a general sense of where the image is with a process called ray tracing: drawing rays from the object to the device, predicting where those rays will go, and finding where those rays intersect (for real images) or where they appear to come from (for virtual images).

Any ray which leaves the object and hits the device will pass through the image, but if we don't know where the image is already, there are two specific rays which are easy to figure out.

1. From the definition of the focal point , we know that any ray which comes in parallel to the axis will either pass through the focal point (for converging devices) or appear to come from the focal point (for diverging devices).
2. Due to symmetry, any ray which hits the center of a lens will pass straight through the lens without being deflected. For a mirror, any ray which hits the center of the mirror will be reflected off at the same angle it came in as (because the center of the mirror is vertical, and the law of reflection holds).
3. The reverse of 1 also works: any ray which comes from the focal point (or appears to come from the focal point) will leave the device parallel to the axis.

You only need two of these three rays to find the image: wherever the rays intersect (or appear to intersect) is the location of the image.

I could draw a number of examples, but it may be better to try out this active simulation and watch what the rays and the image do as you make adjustments.

Try the following:

1. Drag the red bar (the object) side to side to change its position, and drag it up and down to change its height.
2. Try moving the red bar inside the focal point, and see how the image changes from real to virtual. The dashed lines show you where the rays appear to come from.
3. Try dragging on the focal point to change the focal length of the lens. If you drag the focal point to the opposite side of the lens to turn it into a diverging device.
4. You can click the word "Lens" to change it to a mirror (and back again). See how the emitted rays are reflected instead of passing through. Notice that mirrors only have one focal point, instead of two.