But in Jackson’s Classical Electrodynamics, III edition he notes the following:
This is an interesting form of the Laplacian that perhaps not everyone has encountered. This can obtained from the known form by making the substitution and simplifying. The steps to which have been outlined below:
If that wasn’t clear, here is the same demonstration done with Microwaves and using wax as a prism:
The reason why this happens is because the incident wave does not abruptly stop when it hits the end of the prism.
Some of the waves seep out with the intensity of the wave decaying exponentially outside the first prism.
But this changes when you place another prism closer to the first one.
Does this even matter?
You might be tempted to think that this would make no difference on the macro-scale.
One possible application involving TIR and Tunneling are Optical Fibers. Loss of photons (or information) through the cladding layer of an optical fiber due to tunneling is a major concern. Therefore when they are designed the cladding layer thickness is such that the probability of tunneling to occur in such a system is extremely low.
And that’s how Tunneling, Electrodynamics and Optics are interwoven in nature.
**In case you wanted to learn more about this in rigorous manner,most standard graduate level electrodynamics such as Jackson dwell into the mathematics of Evanescent waves. Do take a look at them!
This marvelous display of physics unfolded when tiny charged droplets of water were fired through a syringe towards a needle which was also statically charged. This experiment was conducted at the ISS in 2012.
The droplets remarkably began to orbit the needle, just like some satellites do around a cylindrical planet!
It’s the ISS and things float so, nothing exquisite about that but this demonstration is to illustrate the attraction of charged objects in space..
What is this sorcery?
Since the water droplets and the needle are charged, the droplets are attracted to the needle. But hey, those drops also have some velocity, so they end up orbiting the needle instead of sticking right to it.