Q:  What is the theoretical diffraction limit for this instrument?
              Express your result in arcseconds.

                                  1.63 x 10^(-6) m 
           theoretical limit  =   -----------------  =  1.96 x 10^(-7) rad
                                      8.3 m


                              =   0.041   arcsec

     Q:  At what angular distance from the center of this image
              could astronomers detect an inner planet?
              Look at the noise levels, and express your answer
              in arcseconds.


                  To my eyes, the inner noisy region extends to 

             practical limit  =  approx 0.08 - 0.15 arcsec

 

     Q:  If a planet were present at 1 AU from the host star,
              what would its angular separation be in arcseconds?


                  At a distance of d = 41 pc, a planet at a separation
                  of a = 1 AU would have an angular separation of

                                  1 AU 
                     ang sep  =  ------   =   0.024   arcsec
                                  41 pc



    So it is clear that our instruments on the current big telescopes
are unable to distinguish planets at Earth-like distances from their
host stars, for stars even a few tens of parsecs away from the Sun.