# Why does radio astronomy offer higher resolution images than optical?

According to this lecture,"Radio astronomy has several advantages over optical astronomy...We can make the highest resolution images, and see things happening on the smallest scales."

Why is this? If resolving power, $r \propto \frac{\lambda}{B}$ then shouldn't shorter wavelength light result in smaller angular resolution i.e. better resolution?

If you look at raw resolving power you get for a 10m optical telescope: $\theta_{optical}\approx \frac{5\times 10^{-7}}{10}\approx 5 \times 10^{-8}$ radian. For a synthetic aperture ground based radio telescope operating at 21cm the limiting aperture is of the order of the diameter of the Earth so: $\theta_{21cm}\approx \frac{21\times 10^{-2}}{12\times 10^{6}}\approx 1.75 \times 10^{-8}$ radian. So in this case the resolution of the radio telescope is somewhat better than that of the optical. In the absence of adaptive optics the situation is even more favorable to the radio telescope since we can achieve its theoretical resolution, but ground based optical telescopes are constrained to lower resolutions by atmospheric seeing. Also adaptive optics still do not improve the resolution of optical systems fully to the diffraction limit of the aperture.