An inkjet printer uses tiny dots of red, green, and blue ink to produce an image
ID: 1451479 • Letter: A
Question
An inkjet printer uses tiny dots of red, green, and blue ink to produce an image. Assume that the dot separation on the printed page is the same for all colors. At normal viewing distances, the eye does not resolve the individual dots, regardless of color, so that the image has a normal look. The wavelengths for red, green, and blue are red = 660 nm, green = 550 nm, and blue = 470 nm. The diameter of the pupil through which light enters the eye is 2.0 mm. For a viewing distance of0.71 m, what is the maximum allowable dot separation?
s = _______
Explanation / Answer
given
red = 660 nm, green = 550 nm, and blue = 470 nm
diameter = 2mm
radius=1mm=0.001 m
distance of = 0.71 m
The eye pupil acts as a diffraction aperture - so individual dot images are concentric fringes that overlay on the retina making resolution of detail harder.
The Rayleigh criterion supposes that the two sources are just resolved on the retina when the central diffraction maximum of one source overlays the first minimum of the other .. ie, when the patterns have an angular separation equal to that of the first minimum.
The retina patterns and the dot sources in front of the eye have the same angular separation
for the first minimum from a circular aperture is given by .. sin = 1.22/a
a = diameter of eye pupil = 0.002m
sin = 1.22/a y/0.71m
y 0.71 x 1.22/0.002 = 433.1
If the dots have a separation less than y they are not resolved (appear merged .. as normal).
The smallest y that must not be exceeded is for blue light (smallest )
.. giving a max dot separation y = 433.1 x 470^10-9m
y(max) =0.200mm