Question

When dots are placed on a page from a laser printer, they must be close enough so that you do not see the individual dots of ink. To do this, the separation of the dots must be less than Raleigh's criterion. Take the pupil of the eye to be 3.6 mm and the distance from the paper to the eye of 41 cm; find the maximum separation (in cm) of two dots such that they cannot be resolved. (Assume the average wavelength of visible light is 550 nm.)

Answer 1

Diameter of pupil of eye, d = 3.6 mm = 0.36 cm

Distance of paper from eye, r = 41 cm

Wavelength of light, λ = 550 nm = 550 x 10^-7 cm

According to Rayleigh’s criterion, the maximum angular position at the eye such that the two close objects cannot be resolved is

dθ = 1.22λ/d = 1.22 x 550 x 10^-7/0.36 = 1.863 x 10^-4 rad

if dx the separation between the two dots then

dθ = dx/r

dx = dθ x r = 1.863 x 10^-4 x 41 = 0.0076 cm

the maximum separation of two dots such that they cannot be resolved, dx = 0.0076 cm