Suerat made paintings in which separate dots of color are placed close together on the canvas, and from a distance they merge in the eye to form an image. Consider such a painting with the dots in the painting separated by 1.7 mm and assume that the wavelength of the light is ëvacuum = 500 nm. Find the distance at which the dots can just be resolved by each of the following.

Question

Suerat made paintings in which separate dots of color are placed close together on the canvas, and from a distance they merge in the eye to form an image. Consider such a painting with the dots in the painting separated by 1.7 mm and assume that the wavelength of the light is ëvacuum = 500 nm. Find the distance at which the dots can just be resolved by each of the following. 
(a) the eye (pupils diameter 2.5 mm)

(b) a camera (aperture diameter 25 mm)

drwls · Answer

Use theta = 1.22 (wavelength)/Diameter for the resolution limit in radians. This is referred to as the Dawes' (or Airy) resolution limit.

Let x = 1.7^10^-3 m be the spot size and R be the distance from the painting.

Require that
1.22 (wavelength)/D = x/R

and then solve for R.
wavelength = 500*10^-9 m

(a) When D = 2.5*10^-3 m.
(1.22)*500*10^-9/2.5*10^-3 = 1.7*10^-3/R

Solve for R.

I get R = 7 meters

(b) Repeat the calculation with the larger value of aperture diameter, D.