Answer :
Answer:
14869817.395 m
Explanation:
[tex]\theta[/tex]=22 microarcsecond
λ = Wavelength = 1.3 mm
Converting to radians we get
[tex]22\times 10^{-6}\frac{\pi}{180\times 3600}\ radians[/tex]
From Rayleigh Criterion
[tex]\theta=1.22\frac{\lambda}{D}\\\Rightarrow D=1.22\frac{\lambda}{\theta}\\\Rightarrow D=1.22\frac{1.3\times 10^{-3}}{22\times 10^{-6}\frac{\pi}{180\times 3600}}\\\Rightarrow D=14869817.395\ m[/tex]
Diameter of the effective primary objective is 14869817.395 m
It is not possible to build one telescope with a diameter of 14869817.395 m. But, we need this type of telescope. So, astronomers use an array of radio telescopes to achieve a virtual diameter in order to observe objects that are the size of supermassive black hole's event horizon.