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)

Answer 1

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.