
Every year when I teach the Optics course for physics majors, I start with the treatment of electromagnetic theory and then build on it a variety of optical phenomena and effects. Let me present three aspects related to it:
1. The impact and effect of Heaviside-Maxwell’s equations in understanding how fields can evolve and interact with matter is noteworthy. The foundations of field theory are already there to see, and the arguments of locality and causality take their form in an intuitive way. It shows the power of combining physical intuition with mathematical techniques, and in the process, the flavor of classical physics at its best.
2. To see optics from a framework of a comparison between the wavelength of light and the size of an interacting object. This is usually termed the ‘size parameter’ viewpoint. The size parameter has an intuitive connection to the approximations that we use. For example, the foundation principles on which scattering theory is based for discriminating between Rayleigh and Mie scattering processes are mainly based on size. It is also amazing to see how the dipole approximation can solve or at least give an opening to understand a variety of optical effects. It reveals the power of the method and its effectiveness. Lord Rayleigh had a significant role to play in this way of attacking a problem, and it continues to be one of the most powerful methods to introduce concepts not only in electromagnetic theory but also in applications of quantum mechanics, including atomic and molecular physics.
3. The elegance of mathematics that one must use to understand the electromagnetic theory of light. Of course, a good foundation in vector calculus is necessary, but what intrigues me and several of my students is the effectiveness of vector calculus in trying to understand a variety of processes. Every time we use a Laplacian or a curl of curl type of transformation, we observe how important physical effects emerge from that mathematical operation. One of the most effective ways to study vector calculus is to apply it in electromagnetic theory, and if one needs to broaden the scope of this study, optical effects provide an excellent playground. Ultimately, there is an amazing coherence between what is computed, what is theorized, and what is measured. It is a great model and an advertisement for physics.
Of course, there are many more observations related to teaching this course, which I wish to share, but I will keep them for future blogs. One thing is for sure: there is no end to getting surprised, learning new things, and finally looking at an old phenomenon (literally and metaphorically) in a new light.


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