Refraction
Refraction is what happens to light when it goes from one medium (i.e. a vacuum or air) to another (i.e. glass or water). Most problems in this course in refraction will deal with such situations. The ability of a lens to focus light is derived from nothing more than refraction: Light incident upon a lens from air is bent slightly, and then bent again upon exiting the lens. A prism (which separates light into its different frequency components) works also because of refraction. In the case of the prism, the incident light is bent an amount which depends on the frequency. White light, a sum of all different frequencies, is then spread out as the different frequencies bend different amounts upon going through the prism. In lenses, this tendency of frequency components to separate is known as `chromatic aberration' and is actually quite a concern. Special lenses exist which minimize this aberration.
The reason things happen differently in water as opposed to a vacuum is that light travels at a different speed. Light travels fastest in a vacuum. The ratio of the speed of light in a vacuum () to that in a different medium is called the index of refraction and is usually labelled . For air, is close enough. For water, . For many types of glass, or so. The largest values are greater than 2.0.
We will see shortly how the hypothesis that light always picks the shortest route (time wise) between two points leads naturally to the law of refraction (Snell's law), which I state here:
Let the index of refraction of medium 1 be , and that of medium 2 be . Suppose a ray of light is incident upon medium 2 from medium 1 at angle relative to the normal to the interface between the media. Then the angle that the transmitted ray makes to the normal is given by the following equation:
This is Snell's law. Note that this always means that light coming from a medium with lower index of refraction will always `bend toward the normal' in the medium with higher . In other words, the angle of refraction is smaller than the angle of incidence. This makes sense from the shortest-time standpoint, since if you travel slower in one region than another you'd want to minimize the distance you have to cover in the region. Travelling a little more in the faster medium and then cutting across at a steeper angle through the slower one accomplish this. We'll put this into equations later.
Images
We now turn to the concept of optical images. They are created by systems of lenses and/or mirrors, and have the following characteristics:
Real or virtual: If the rays appear to come from a point in space, the image is virtual. If the rays go towards a point in space (converge there), then the image is real.
Upright or inverted: Real images are always inverted. Virtual images are always upright.
Magnification: The size of the image relative to the size of the object that created it.
Position: Where is the image (or where does it appear to be)?
To determine these characteristics, we follow a simple set of rules:
(a)
Take 2 different rays, both coming from the same point on the object.
(b)
See if they converge or diverge.
(c)
Take a third ray to verify the image.
(d)
Use ``simple" rays.
Important formulas
I end this lecture by reminding you of some important formulas for mirrors. Remember that is the position of the image, and is the position of the source. Is the magnification, the radius of curvature?
Magnification
Angular magnification
The magnification of an optical instrument is given by the angular magnification of the lens combination. Angular magnification is the ratio of the angular size of the image to that of the source. The angular size of something is its actual size divided by its distance from your eye. For example, the moon's angular size is about one degree.
