I have stated this many times on this bbs, even quoting numbers from my own calculations. To pick up radio stations from earth at a distance of 4.3 lightyears would require an antenna 3-times the diameter of our solar system. To see city lights on a planet 74 lightyears away would require an optical mirror 414.7 kilometers in diameter.

The equation describing telescope resolution is:

alpha = 20 * w / b

where,
alpha = angular resolution in arcseconds
w = wavelength of radiation observed in micrometers
b = diameter of mirror (or baseline of interferometer) in centimeters

I would do the calculations again, but I am sure PhilW's pocket calculator is more accurate than mine. LOL