When the size of the physical and optical objects of a system are much larger than the wavelength of the light (or as λ→ 0 ), we are in the realm of geometrical optics. Optical systems in which the wave nature of light must be taken into account (interference, diffraction) are called physical optics. Of course, every real system experiences diffraction effects, so geometric optics is necessarily an approximation. However, the simplicity arising from treating only rays which move in straight lines affords many uses.
A lens is a refracting device (a discontinuity in the medium) that redistributes the energy being propagated by electromagnetic radiation. This is usually achieved by re-shaping the wavefront, most usefully by turning spherical waves into plane waves and vice-versa. Lenses that cause an incoming plane wave to bend towards the axis through its middle are called converging or convex lenses. They are thicker at their midpoint than at their edges. Concave lenses, on the other hand, are thicker at their edges than in the middle; they cause an incoming plane wave to bend away from its central axis and are hence also known as a diverging lenses. Both of these are illustrated in .
Lenses that have only two refracting surfaces are called simple. Also, lenses that have a thickness that is negligible compared to the overall path length of the light traversing them are called thin. Here we will only consider thin, simple lenses. To first-order, the focal length of such a lens is given by:
|= (n l -1) -|
By far the most important formula in geometrical optics, however, relates the position of an object placed in front of a lens to the position of its image, formed by the lens. In the distance between the object and the lens is s o and the distance between the lens and the image is s i .
|M T = = -|
There are also two basic types of spherical mirrors. Concave mirrors reflect incoming plane waves to a focal point directly in front of the mirror (they are converging mirrors). Convex mirrors reflect incoming plane waves into outward-moving spherical waves with the center of the sphere appearing to be behind the mirror (they are diverging mirrors).
Mirrors have an advantage over lenses in that they do not suffer chromatic aberration. This phenomenon arises due to dispersion, causing the lens to have not just one focal length but a small band of focal lengths corresponding to the different amounts by which it refracts the different colors. This means that it is impossible to focus colored images precisely with a lens. Mirrors, because they do not rely on refraction, do not suffer this problem. Moreover, it is important to remember that all the formulas we encountered here were derived using the first order approximation to the sine function appearing in Snell's Law: sinθ θ . Of course this ignores higher order terms in θ 3 , etc. Corrections arising from this and other considerations cause aberrations (or deviations) from the simple equations developed here for spherical lens and mirror systems. In fact, there are five primary, monochromatic aberrations called spherical aberration, coma, astigmatism, field curvature, and distortion. They are collectively known as the Seidel aberrations.
Often it will be useful to determine the approximate position of an image, given the position of the object and the focal length in a lens or mirror system without resorting to the lens equation. We can do this by drawing diagrams and mapping out the path of the light rays. This process is known as analytical ray tracing. The basic strategy is to select a significant point on the object (like the top) and to draw several principal rays from that point. For a mirror, the three principle rays, shown in , are: i) parallel to the axis, returning through the focal point; ii) to the midpoint of the mirror, reflecting at an equal angle on the opposite side to the central axis; and iii) through the center of the sphere of which the mirror is a part, returning along the same path.
Ray tracing is especially useful when complicated systems of mirrors and/or lenses need to be analyzed. Ray tracing can give a rough but quick idea of how the system will behave. For example, it can fairly quickly be determined that a single concave lens will always produce virtual, diminished, upright images, irrespective of the position of the object. However, for a convex lens, the location of the image depends on the location of the object. Recall that real objects and real images have s o > 0 , or s I > 0 , while these distances are negative for virtual objects and images (virtual objects can arise when the image for one lens becomes the object for another in a lens system). f > 0 corresponds to converging lenses or mirrors and f < 0 corresponds to diverging lenses or mirrors. Positive y o or y i correspond to upright objects and images respectively. A negative magnification corresponds to an inverted image.