An astronomer wishes to study a close binary star whose components are separated by only 1.0 arc–second. The observations are to be made with a telescope placed at a high mountain site where the atmosphere provides a seeing disk of 0.50 arc–second.
(i) Express 1.0 arc–second in radians, giving your answer correct to two significant figures.
(ii) Determine the minimum diameter of the telescope objective that will barely resolve the binary when observations are made with blue light of wavelength 450nm.
(iii) If the same telescope is used with red light of wavelength 700nm, find the new resolving limit set by the instrument alone and state whether the binary will still be resolved.
(iv) Discuss, with calculations where necessary, whether increasing the objective diameter beyond the value obtained in part (ii) will improve the actual detail seen, taking the given atmospheric condition into account.