Consider the following model:

a) Assume a spherical earth.

b) Assume that the ionosphere is a spherical mirror that is concentric with the center of the earth. For the purpose of this question, we assume the mirror is perfect and there are no other atmospheric distortions present that might alter the path of a signal.

c) A transmitter and receiver are co-located at some point on the earth's surface and a vessel is positioned 1000 km away.

d) The transmitter broadcasts a signal which is reflected of the ionosphere with part of the signal then being reflected back by the aforementioned vessel.

e) The signal reflected of the vessel bounces of the ionosphere and is detected by the receiver.

Question: Would the signal that is detected by the receiver have followed the same path as the signal broadcast by the transmitter?

Those around me think that the transmitted and received signals follow the same paths.

I've modelled this scenario myself and my model suggests that the transmitted signal would follow a slightly different path to the received one. Further still, according to my model, the deviation between the paths decreases as the distance between the transmitter/receiver and the vessel increases. Also, the deviation between transmit signal azimuth and receive signal azimuth varies as the placement of the vessel is changed.

I've spent time trying to find an answer to this problem on the internet but could find none. I'd have thought this would be a classic ray tracing problem.


A thought experiment: can you look in a mirror and see a person without them being able to see you? What about if you had two mirrors? Curved mirrors?

When it comes to electromagnetic radiation, the laws are symmetrical.

Of course, its also worth noting that when we talk about waves, like RF waves, a signal does not take a path. A signal takes all paths. The receiver will receive the transmission across all paths between the points. Some will be much stronger than others, but all paths will be taken.

Now with a real ionosphere, rather than a mirror, we're going to have to invoke black magic to explain what reflections are available at any time, and how they change while you are transmitting. But for the simplified case symmetry rules the day.


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