An x-ray telescope with a 1.18 m diameter mirror is in an orbiting satellite above the atmosphere. If an approaching object 3.89 Gm away emits monochromatic x- rays of frequency 1.65x1018 Hz, find the minimum separation distance, in m, theoretically resolvable with this telescope. NOTE: This gives one reason why high frequency telescopes are so valuable. However, they cannot be used on Earth, since x-rays are almost completely blocked off by our atmosphere.

angular resolving power of a X-ray telescope is given by

$$\begin{gathered} {\theta }_{min}=\frac{1.22\lambda }{D} \\ where D is the diameter of the aperture, \lambda is the wavelength of the light to be resolved \\ here, \lambda =\frac{c}{\nu }=\frac{3\times {10}^8}{1.65\times {10}^{18}} \\ =1.818\times {10}^{-10}m \end{gathered}$$

$$\begin{gathered} {\theta }_{min}=\frac{1.22\times 1.818\times {10}^{-10}}{1.18} \\ =1.88 \times {10}^{-10}rad \\ given D=1.18m \end{gathered}$$