Plz help with this physics question

Question

The dots in the painting are separated by 1.7 mm and that the wavelength of the light is the wavelength of vacuum=530 nm. Find the distance at which the dots can just be resolved by (a) the eye and (b) the camera. Also, the pupil of his eye has a diameter of 2.5 mm.

Answer 1

Use the Rayleigh Criterion

The Rayleigh criterion is the generally accepted criterion for the minimum resolvable detail - the imaging process is said to be diffraction-limited when the first diffraction minimum of the image of one source point coincides with the maximum of another.

For a circular aperature:

sin(angle of resoultion) = 1.22 (wavelength/diameter of aperature)

sin(angle) = 1.22(530 x 10^-9m/2.5 x 10^-3m) = 1.22(212 x 10^-6)

sin(angle) =258.64 x 10^-6

angle =arcsin(0.00025864)= 0.000258640003 radians

r=  (arc length)/ angle

r= 1.7 x 10^-3 m /  0.000258640003 radians  

r=6,572.84248 x 10^-3 m = 6.57 m