Question

Two stars 19 light-years away are barely resolved by a 63 cm (mirror diameter) telescope. 1ly=9.461×1015m.How far apart are the stars? Assume λ = 550 nm and that the resolution is limited by diffraction.

d=_____? m

Answer 1

Resolution of the Telescope is given as :

= (1.22) / D                                           { eq.1 }

where, = wavelength = 550 x 10^-9 m

D = mirror diameter = 0.63 m

inserting these values in above eq.

= (1.22) (550 x 10^-9 m) / (0.63 m)

= (671 x 10^-9 / 0.63) radian

= 1065.07 x 10^-9 radian

= 1.06 x 10^-6 radian

separation distance of the stars will be given as ::

d = L                                                                      { eq.2 }

where, L = 19 ly = 19 x 9.461×10¹⁵ m

inserting the values in eq.2,

d = (19 x 9.461×10¹⁵ m) (1.06 x 10^-6 rad.)

d = 190.54 x 10⁹ m

d = 1.9 x 10¹¹ m