This chapter will be our first look at how light interacts with matter. As it turns out, the study of light's interaction with matter is one of the most interesting and complex studies in nature, and physicists still have lots to learn in this realm. There are many levels at which this topic may be approached. This will be the most elementary view, but as we progress through the course we will take other views of this fascinating topic.[br]Geometric optics has its name since the rules are based on simple empirical laws coupled with geometry. An [i]empirical[/i] law is one derived from experience or measurement rather than from fundamental understanding of a subject. I like empirical laws for their usefulness (which is why they exist in the first place), but what I don't like is that they work like magic. As a theoretical physicist I always want to know why empirical laws work the way they do based on the most fundamental principles in nature. I will share such understanding with you in any case where the extra effort doesn't require math that's beyond your level of education and where it won't take a huge amount of time away from the other material that we need to discuss this semester. I hope you come to appreciate these brief detours.

As I mentioned, there are many levels from which we can view light's interaction with matter. While you may know that light is a wave, that is not the whole truth about light. In fact I will show you this semester that light has three faces. In a very real sense light is not even a duality as just about every text on physics mentions, but is rather a trinity - or three distinct and measurable natures in one! If there is one entity in nature that is confusing to think about, it is light. [br][br]Right now we will treat light as something that travels like a stream of water out of a squirt gun - except that it will not fall under the influence of gravity. Having said that, I should mention that light [i]does[/i] fall under the influence of gravity, but not in a way that you and I would ever notice while playing with light in the context of geometric optics. This view of light that travels like a stream of water is called a [b]light ray[/b]. As it turns out, a ray is not any of the fundamental natures of light, but is most closely related to its wave nature as you'll see near the end of this chapter. So light rays are fictitious. They are kind of like empirical laws in the sense that they are not born of understanding, but of usefulness.[br][br]What a light ray does for us is shows us the path along which light travels as it passes between materials, through materials or reflects off of materials. We draw light rays with lines and arrows much like we draw vectors. The difference is that light rays can bounce and bend whereas vectors can't have kinks in them. The only time we see light rays bounce and bend is when there is a change in the properties of the medium through which the light is traveling. So when light passes from air into water or from water through glass, or from cool air to hot air, we will expect it to bend or bounce.

The term reflection is given to the "bounce" scenario. If you have ever seen your reflection in a mirror, then you have witnessed light bouncing, or reflecting, off a surface. The mirrored surface is usually a smooth metallic layer, but technically just about anything will work to reflect light - it just might not reflect all wavelengths as well as most metals do.[br][br]When light reflects off a surface it does so according to a simple empirical law: The incident angle of the ray with respect to the surface normal (a unique vector to describe surface orientation) will equal the reflected angle, or [math]\theta_{incident}=\theta_{reflected}.[/math]

The law of reflection is true of any surface that reflects light. How do you know if a surface reflects light? If you can see it, and if it is not a glowing source of visible light, then it reflects light. You may be reading that last line and feeling troubled (or suspecting I'm making a mistake) since we don't use things like cotton t-shirts for mirrors in our homes. The real reason for that is not that cotton doesn't reflect light, but that it does so in what's called a [b]diffuse[/b] fashion. The problem is that cotton is not smooth in the way that polished aluminum is. Look at it under a magnifying glass. It has lots of hairs and fibers and is literally woven into fabric out of strands just like most clothing materials. Compare that to a polished piece of metal which has no ridges or valleys and you see immediately what the difference is. If a material is highly polished or smooth, then it reflects in what's called a [b]specular[/b] fashion. On the surfaces of both materials the law of reflection is obeyed, but the incident angle for parallel rays varies dramatically for the cotton and not for the smooth metal. This sends the cotton reflected rays in all directions. This random scattering of light rays from a cotton t-shirt removes all hope of forming an image like you'd see in a mirror. We'll soon see why.

You probably have the belief that you can see depth. Any such sensation is a construct of your mind. What I mean by this specifically is that you might have the idea that you can detect far-away objects while they are at a distance. You might think you can detect the sun that's [math]1.5\times 10^{8}km[/math] away with your eyes. You can do no such thing! [br][br]To "see" the sun you must wait for light to leave the sun, travel all 150 million kilometers through outer space to earth, enter earth's atmosphere, travel all the way through that atmosphere nearly to the ground, enter into your eyeball and strike the back surface of your eye called the retina. This transit of the light takes around 8 minutes. So what did you "see"? Seeing is light striking the back of your retina. Did you see the light when it was as distant as the sun? Of course not. Vision takes place after light strikes your retina. When the light strikes receptor molecules, they send an electrical signal down the optic nerve to your brain and your brain has to figure out what to do with that data caused by light striking the retina. [br][br]The perception of depth is possible not because any data is contained within the light about the travels it's been on (no such information exists), but rather because it strikes both of your eyes. This gives your brain an extra piece of information. In order for the image from your left eye to match the image seen from your right eye, your eyes must be carefully aligned. There are muscles to do that alignment job, and your brain can track the alignment of the eyes. In order for nearby objects' images to overlap, your eyes must cross a little and alignment is not quite parallel. Your eyes are crossed. As objects become more distant they cross less and less. It is the amount of the crossing of the eyes that gives the brain the geometrical information it needs to reconstruct the sensation of depth. Besides this, even with one eye open it'd seem like you can see depth. That is almost entirely based on your knowledge of the size of familiar objects. When familiar objects appear small we assume they are distant. [br][br]The brain can be fooled about where objects are located. This is really what images are all about. Since light doesn't contain information about where it has been and how it has bounced around or bent along its path, [b]the brain must assume that light has been traveling in a straight line since it originated[/b]. This allows us to see things that aren't really there - like a person that looks a whole lot like you brushing his or her teeth in the morning while you look in the mirror. He or she sure looks real, but is not really there! [b]The images we see while using optical devices are always found by considering the question "Where does light seem to have originated if I track its path back as if it traveled along straight lines?".[/b]