The radio telescopes that make up the VLA (Verry Large Array) in New Mexico each have a diameter of 25 m. What is the smallest angle they can resolve when observing at a wavelength of 1 cm? If Mars has a diameter of 30", can Mars be resolved? The telescopes of the VLA can be strung out to have a maximum separation of 27 km. How much better is the resolution if the signals from the antennas are combined using the techniques of radio interferometry compared to the resolution of a single dish?
The formula for the minimum angular resolution of a telescope is 1.22/D, where is measured in radians. Plug in our values for the size of the radio telescopes and the wavelength of radio waves:
= 1.22(1x10-2 m/25 m) = 5 x 10 -4 radians
5 x 10 -4 radians * (206,265"/1 radian) = 100"
Since 100" is larger than the angular size of Mars (30") it CANNOT be resolved.
The images made by the telescopes in interferometry mode will have the effective resolution of a telescope the size of their spacing. Thus, since the maximum separation of the telescopes is ~ 1,000 times bigger than the individual telescopes the resolution will also be ~ 1,000 times smaller.
2/1 = D1/D2 = (25 m/27 x 103 m) 1 x 10-3
2 = 1 x 10-3 1 = 0.1"