Question

When reading the printout from a laser printer, you are actually looking at an array of tiny dots.

If the pupil of your eye is 4.2 mm in diameter when reading a page held 29 cm from your eye, what is the minimum separation of adjacent dots that can be resolved? (Assume light with a wavelength of 500 nm , and use 1.36 as the index of refraction for the interior of the eye.)
Express your answer using two significant figures.

Answer 1

Answer:

The value is $y = 3.097 * 10^{-5} \ m$

Explanation:

From the question we are told that

The diameter of the pupil is $d_p = 4.2 \ mm = 4.2 *10^{-3} \ m$

The distance of the page from the eye $d = 29 \ cm = 0.29 \ m$

The wavelength is $\lambda = 500 \ nm = 500 *10^{-9} \ m$

The refractive index is $n_r = 1.36$

Generally the minimum separation of adjacent dots that can be resolved is mathematically represented as

$y = [ \frac{1.22 * \lambda }{d_p * n_r } ]* d$

         $y  = [ \frac{1.22 *  500 *10^{-9} }{4.2 *10^{-3} * 1.36} ]* 0.29$

         $y  = 3.097 * 10^{-5} \  m$