Can a lens be used at radio frequency? Lenses and Antennas are two means of manipulating EM waves. While antennas are predominantly used at RF / Microwave frequencies, Lenses are used for optical/IR regions of the spectrum.
I understand why antennas aren't used at optical/IR frequencies: an optimal antenna should have a length on the order of the wavelength. For a nm to um wavelength, the resulting antenna would be too small to be practically useful.
But I don't see a reson why lenses typically used for optical/IR frequencies aren't used in everyday life for RF/microwave. Apart from optical coatings, I see no fundamental reason. Lens's focal length is independent of frequency, and Air's index of refraction doesn't seem to be changing significantly with frequency.
 A: While not common today, many radars of the 1950s used a lens instead of a parabolic reflector or similar. A typical arrangement used a series of short metal tubes arranged into a grid so that their open ends were pointed towards the “line of shoot”. The signals slowed as they travelled down the open tubes, so by cutting each one to a different length, the lens could be shaped as desired. The AMES Type 82 used this arrangement, you can see it in the wiki article on the topic. Some US radars of the era used a variation made with many thin metal plates in a venitian blind like arrangement. The Nike Ajax used this arrangement.  They fell from use largely because reflectors had fewer losses and were easy to build. 
A: The answer is yes. Lenses are used. Here is an example of a commercially avaliable lense for 500 GHz:
https://www.thorlabs.com/NewGroupPage9.cfm?ObjectGroup_ID=1627
Here some others:
http://www.tydexoptics.com/products/thz_optics/thz_lens/
(This is calculated up to 3mm wavelength so 100 GHz)
So lenses are successfully used in Thz and short mm wave applications. While there is no hard limit it seems usually people start at W Band (75 GHz). You want your lense to have the diameter of a few wavelength, so at some point lenses get more cumbersome to use.
Imagine 10 Ghz so 30mm wavelength, then the lense shd br around 30cm diameter. Probably somebody tried this, but it gets unpractical at some point.
A: 
Lens's focal length is independent of frequency

This is not true; a lens's focal length varies depending on frequency, this is why prisms work and why chromatic aberration exists. Radio waves have a very different index of refraction through glass than visible light.
As to your question, 'lenses' for RF do exist, they are called dielectric resonators. Even though they work based on 'refracting' RF waves, the rules of geometric visible light optics don't apply. They are designed based on different rules.
