Question Why do radio telescopes not have polished surfaces like optical telescopes?
Answer Radio telescopes do have polished surfaces, it just does not have to be to the same polished level as that of an optical telescope.
For all telescopes, we want as much detail as possible, but the different wavelengths means they have different sensitivity limits. All colors of light (X-Ray, UV, Optical, Radio) travel at the same speed (the speed of light), but because of their varying wavelength (how big or small they are), you need to have a different level of precision, relative to the length of the wave. When you create a telescope, you therefore have to make the surface/instrument as sensitive as the wavelength.
For example, if you want to build an optical telescope where the light is on the scale of nanometers, making a mirror that is only sensitive to meter wavelengths means you won't get any information. However, you do not need to make an optical telescope surface any better than nanometers, as you won't gain any extra information as the physical limit has a wavelength. Same example but for an infrared telescope. Infrared light is on the order of micro-meters, so having a surface only good to meters is not good enough, and nanometers is too good.
FYI, I know this is your homework question that you submitted previously and re-worded, so I'm not giving you a direct answer for your homework question.
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