I want to substitude the ray optics analysis with what are the resultant waves that happen. I say "resultant" because many waves that would exist if they were alone, as they are not alone, after their superposition with the other waves become some resultant waves which are not the same with each wave that would exist if it was alone.

Question

I want to substitude the ray optics analysis with what are the resultant waves that happen. I say "resultant" because many waves that would exist if they were alone, as they are not alone, after their superposition with the other waves become some resultant waves which are not the same with each wave that would exist if it was alone.

E.g. The many straight rays going from the object to all the areas of a flat mirror should be the equivalent of one shperical wave radiated from the source i.e from the object that its image can be seen inside the mirror. Or it should be the resultant waves of the many spherical waves, as the object is not a point-source but many point sources (say atoms) and each atom radiates a shperical wave. And the many straight rays reflected from the mirror should be...and then the superipotition of all these should be.... At the second applet of this link:
h t t p : / / w w w. cabrillo.edu/~jmccullough/Applets/Applets_by_Topic/Superposition_Interference.html
put a wall-mirror in front of the source-object. Where are all these straight lines of ray optics? Would I see them if I substitude the point source with many point sources (the atoms of the object) close together?
Do you know any link that has done this job of substituting ray optics analysis with waves? I.e. all this stuff with the lenses and the why something can be photographed because the rays were such and such?

Answer 1

I think you are missing the point.

First of all, consider Huygens' principle:

Here it is as differential equations:
http://www.mathpages.com/home/kmath242/kmath242.htm

The entire principle says that each point of any wave is a wave front for a new wave. Ray diagrams just draw the direction of propagation as a line, it still is a wave, traveling in the form of a wave. What about all the other waves? They don't end up in your eye, so you don't see them.

Answer 2

To substitute ray optics analysis with wave analysis, you would need to consider the wave nature of light and the principle of superposition. In ray optics, you consider light as a collection of straight rays that undergo reflection, refraction, and other phenomena. However, in wave optics, light is considered as a wave that propagates through space.

To understand the resultant waves that occur when multiple waves superpose, you can use the principle of superposition. This principle states that when two or more waves overlap, the resulting wave at any point is the algebraic sum of the individual waves at that point.

For example, when considering the reflection of light from a flat mirror, instead of only considering the straight rays using ray optics, you can analyze the situation using wave optics. A flat mirror can be thought of as a surface that reflects light waves. When a plane wave (spherical waves can be approximated as plane waves over small distances) interacts with the mirror, it reflects off at the same angle of incidence. The reflection can be understood as the superposition of the incident wave with the reflected wave, resulting in a resultant wave.

By considering the wave nature of light and using the principle of superposition, you can analyze various optical phenomena, such as interference, diffraction, and refraction, which cannot be explained solely by ray optics.

Regarding your question about substituting the point source with many closely spaced point sources, this approach is indeed used in wave optics to describe complex wavefronts. When the source object is not a point source, but consists of many point sources close together, you can consider each point source to emit a spherical wave. The superposition of all these spherical waves will result in a complex wavefront, which then undergoes reflection, refraction, or other interactions with optical elements.

As for links or resources that explain this topic further, there are several textbooks and educational websites that cover wave optics, including interference and diffraction. Here are a few recommendations:

1. "Principles of Optics" by Max Born and Emil Wolf
2. "Introduction to Optics" by Frank L. Pedrotti, Leno M. Pedrotti, and Leno S. Pedrotti
3. Khan Academy's Optics section: https://www.khanacademy.org/science/ap-physics-2/waves-and-optics

These resources will provide more in-depth explanations and examples of wave optics, including the concepts of superposition, interference, and diffraction.