Geometrical optics is just an approximation.

Law of reflection: the light striking a mirror travels in such a way that the two angles, between each beam and the mirror, are equal.

The principle of least time, or Fermat's principle: out of all possible paths that it might take to get from one point to another, light takes the path which requires the shortest time.

An ellipse is that curve which has the property that the sum of the distances from two points is a constant for every point on the ellipse; thus we can be sure that the light from one focus will come to the other.

Parabola  is the locus of all points equidistant from a line and a point.

We predict that the index for a new pair of materials can be obtained from the indexes of the individual materials, both against air or against vacuum.

Geometrical optics is a most useful approximation in the practical design of many optical systems and instruments.

When we look at the bottom of a swimming pool from above, it does not look as deep as it really is, by a factor 3/4, which is the reciprocal of the index of refraction of water.

Any optical instrument - a telescope or a microscope with any number of lenses and mirrors - has the following property: There exist two planes, called the principal planes of the system (these planes are often fairly close to the first surface of the first lens and the last surface of the last lens), which have the following properties: (1) If light comes into the system parallel from the first side, it comes out at a certain focus, at a distance from the second principal plane equal to the focal length, just as though the system were a thin lens situated at this plane. (2) If parallel light comes in the other way, it comes to a focus at the same distance f from the first principal plane, again as if a thin lens where situated there.

The limitations of a microscope are not that it is impossible to build a lens that magnifies more than 2000 diameters.

The energy that we can take out of the wave within a given conical angle is the same, no matter how far away we are! In particular, the total energy that we could take out of the whole wave by putting absorbing oscillators all around is a certain fixed amount.

The angular frequency can be defined as the rate of change of phase with time (radians per second). The wave number is defined as the rate of change of phase with distance (radians per meter). The wavelength is the distance occupied by one complete cycle. By the intensity we mean the amount of energy that the field carries past us per second, which is proportional to the square of the field, averaged in time.

The sum of two cosines is twice the cosine of half the sum times the cosine of half the difference.

No one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them. The best we can do, roughly speaking, is to say that when there are only a few sources, say two, interfering, then the result is usually called interference, but if there is a large number of them, it seems that the word diffraction is more often used.