   Chapter 27, Problem 67PE

Chapter
Section
Textbook Problem

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 3.0 mm and the distance from the paper to the eye of 35 cm; find the minimum separation of two dots such that they cannot be resolved. How many dots per inch (dpi) does this correspond to?

To determine

The minimum separation of two dots such that they cannot be resolved and also, the number of dots per inch.

Explanation

Given info:

Diameter of the pupil is, D=3.0mm.

Distance from the paper to the eye is, d=35cm.

Average wavelength of visible light is, λ=550nm.

Formula used:

The expression for the Rayleigh criterion is,

θ=1.22(λD)

Calculation:

By substituting the given values, in the above expression, we get

θ=1.22( 550× 10 9 m 3.0× 10 3 m)θ=2

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