Fraunhofer diffraction for a small obstracle

[Mahasweta]

1. Two towers built on hills are 50 km apart and the line joining those passes above a hill midway between them. what is the longest wavelength of radio waves which can be sent between the towers without serious diffraction effects caused by the central hill?


2. Is the width of the obstrucle in necessary?



3. I think the problem can be related to Fraunhofer diffraction for a small obstracle. The condition for this type of diffraction is R≥ a^2/λ. But this requires the maximum width of obstracle.

 

[Simon Bridge]

If the transmitter used extremely short wavelengths - what would happen?
Notice that the line joining the towers passes above the hill.

 

[Mahasweta]

But in case I want some approximate numerical value of the wavelength that can pass without any diffraction effect? What should I do?

 

[Simon Bridge]

But in case I want some approximate numerical value of the wavelength that can pass without any diffraction effect? What should I do?

What you do, to start with, is answer the question in post #2. You should also follow suggestions.
I'll only show you one step at a time because you are the one who has to take the steps, and everyone's path is different.