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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 .

Figure %: Concave and convex lenses.

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) - |

where

Figure %: Derivation of the lens-makers equation.

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}.

Figure %: The Gaussian Lens Formula

+ = |

There are certain sign conventions to be applied with this formula, and with those to follow.

M_{T} = = - |

From the sign conventions,

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).

Figure %: Concave and Convex mirrors.

= + |

Applying the sign conventions that

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: sin*θ**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.

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