Light is electromagnetic energy traveling in a transverse wave form in a straight line
whose direction is normal(perpendicular) to the wavefront. Light in a vacuum travels
at a velocity, c= 3 x 10⁸ meters/second. In any other material this velocity is reduced.
The ratio of the velocity of light in a vacuum V_v to the velocity of light in a material V_m
is known as the index of Refraction, N_m of that material.

N_{m =} V_v / V_m

There are two typical surfaces. One of these is the interface between a transparent
material (i.e., air or glass) and an opaque metal. A light incident on the surface will
be partially reflected and partially absorbed by the metal. The fraction of the incident
light reflected by the metal is known as the reflectance of that material.

Fig. 1 reflection from the metal surface

The other surface is the interface between two transparent materials with different
indices of refraction such as air and glass. Light incident onto this surface from a
less dense, lower index material to a more dense material is partially reflected and
partially transmitted according to Fig. 2.

Fig. 2 reflection and refraction (lower index to higher index)

Light incident onto the surface from the more dense, higher index material to the
less dense material is partially reflected and partally transmitted accirding to Fig. 3,
if the angle of incidence is less than rhe critical angle.

Fig. 3 reflection and refraction (lower index to higher index) with angle of
          incidence less than the critical angle

Light incident onto the surface from the more dense, higher index material to the
less dense material at an angle of incidence greater than the critical angle the light
will undergo a total internal reflection.

Fig.4 total internal reflection

A refrating prism can be used to seperate wavelengths. Knowing the prism anges
the angle of incidence and the index of refraction the angles of the refraction at each
surface can be calculated by using the formulars given above. Because the index of
refraction changes with wavelength so do the angles of refraction at each surface.

Fig 5 Dispersing prism

Total internal reflection is used in reflecting prism. Here the internal angle of incidence
at the reflecting surface is greater that the critical angle.

Fig. 6 90¡Æ Reflecting prism

Lens operation

A simple (one element) lens is a transparent optical material, such as glass or fused
silica with two surfaces either concave, convex or flat.

A lens will accept collimated (parallel) rays and focus them to a point at a distance
of one focal length from the lens according to the general lens maker's formular given.

Fig. 7 Lens markers formulas

A planoconvex lens is a special simplifying case.

Fig.8 Lens markers formulas -plano-convex lens

Light rays sre reversible through a lens so that a point source at a distance of one
focal length will produce a collimated (or parallel) beam. The degree of collimation
will depend on the size of the source and the focal length of the lens.

Fig.9 Angle of collimation

If the light source or object is moved further away a real image of that source or
object is created. A real image is one which will appear on a screen placed at the
image point.
A source of finite size will produce an image of a size that can be calculated.

Fig.10 Object and image distance

If the source is moved closer then one focal length, a virtual image is formed.
A virtual image will not appear on a screen but can be seen by looking through the lens.
(This is a " magnifying glass".)

Fig. 11 Virtual imaging

Diverging or "negative" lenses, plano-concave or biconcave, have tha same lens
maker's formulars as the convex lens as long at the sign convention is maintained.
A collimated (parallel) beam entering a concave lens will create a virtual image at
one focal length.

Fig. 12 Diverging lens

the aperture of a lens can be defined as it's focal ratio or "F number" or f/no.
The light gatering ability or thoughput of a lens is given.

Fig. 13 Lens aperture

Calculation for an optical train of two or more lenses can be done serially.
The image from the first lens becomes the object for the second, etc.

Fig.14 Lens combinations

Two lenses for focal length f1 and f2, placed close together will act as a single lens
with focal length, f.

Fig. 15 Multi - element lens

For most energy transfer and on-axis or non critical imaging applications spherical
aberration and chromatic aberration are significant and are discussed here.

Spherical aberration results from the fact that a spherical shape, although
economically practical is only approximation for a perfect lens. The lens maker's
formula in Fig. 7 predicts the focal length for the paraxial rays (rays close to the axis)
only. The focal length for the edge rays is generally shorter. The magnitude of the
spherical aberration depends on the distance of the rays from the center line therefore
is more significant with low f/no. lenses. For all but the most critical applications the
spherical aberration of lenses above f/6 are small.

Fig.16 Spherical aberration

using the best available lens shape and orientation. For a given single
(single element lens the lowest spherical aberration is obtained when the angle of
incidence of the entering ray at the edge equals the angle of refraction of the exiting ray.

Fig. 17 and 18 Best shape and orientation

Use more than one element. By using four surfaces instead of two the total spherical
aberration is reduced.

Fig.19 and 20 Using two element lenses

An aspheric lens whose shape is designed for zero spherical aberration even at
low f/no's. A high quality ground and polished aspheric lens is extremely expensive
but for non critical very low f/no. applications (such as condensing lenses) an
inexpensive molded aspheric lens may be the best choice.

Fig. 21 Aspheric lens

A multi-element lens with one negative element: the spherical aberration of the
negative element is just matched to the sum of spherical aberration of the positive
elements.

Fig. 22  Aspherab multi element lens

The index of refraction of optical materials varies with wavelength (higher indices with
shorter wave lengths) A simple lens will have shorter focal lengths for shorter
wavelengths.

Fig. 23 Chromatic aberration:simple lens

This can be corrected by a compound lens of a positive and negative element just
equals and cancels that the positive element. Two element lenses are normally
corrected for two wavelengths and exhibit a small account of chromatic aberration
at the other wavelengths within the range.

Fig. 24 Achromatic lens

A concave reflector can often be substituted for a lens as a focussing element with
the advantage of wide wavelength response and no chromatic aberration. Object to
image distance ratios and image distance ratio and image magnification operate
similarly to that of lenses.

Fig. 25 Concave mirrors