Question

When dots are printed from a laser printer to form letters, 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 of your eye at distances typical for reading Randomized Variables D 2.5 mm d-38 cm Take the pupil of the eye to be 2.5 mm in diameter and the distance from the paper to the eye as 38 cm. Find the minimum separation of two dots such that they cannot be resolved in cm. Assume a wavelength of 555 nm for visible light.

Answer 1

The minimum separation is
`z = 1.0292 *10^(-4) \ m`

Explanation:

From the question we are told that

The reading randomized variable are
`D= 2.5 \ mm` and
`d = 38 \ cm`

The diameter of the pupil is
`d = 2.5 \ mm = (2.5)/(1000) = 0.0025 \ m`

The distance from the paper is
`D = 38 \ cm = 0.38 \ m`

The wavelength is
`\lambda = 555 \ nm = 555 * 10 ^(-9) m`

Generally the Raleigh's equation for resolution is

`\theta = 1.22 [(\lambda)/(D) ]`

substituting values

`\theta = 1.22 * (555*10^(-9))/(0.0025)`

`\theta = 2.7084*10^(-4) \ rad`

The minimum separation of two dots is mathematically represented as

`z = \theta d`

substituting values

`z = 2.7084*10^(-4) * 0.38`

`z = 1.0292 *10^(-4) \ m`