You are watching the latest Star Wars trailer (full screen, of course), and noti

Question

You are watching the latest Star Wars trailer (full screen, of course), and notice that a few individual pixels scattered across the image seem to spell out a message, "Jar Jar lives." You think perhaps your eyes are deceiving you, so you consider the physics.

The monitor measures 14.16-inches (0.360-meter) across the diagonal, and is 1024 pixels wide and 768 pixels tall. Each pixel is a square approximately 281 micrometers on each side. Up close, you can see the individual pixels, but from a distance they appear to blend together and form the image on the screen.

Part A

If the maximum distance between the screen and your eyes at which you can just barely resolve two adjacent pixels is 1.30 meters, what is the effective diameter d of your pupil? Assume that the resolvability is diffraction-limited. Furthermore, use =550 nanometers as the light wavelength for the pixels in question. (Answer=3.1 mm)

Part B

Troubled by this hidden message, you flee your computer. At what distance can you no longer resolve two pixels on diagonally opposite corners of the screen, so that the entire screen looks like a single spot? Note that the size (0.360 meters) quoted for a monitor is the length of the diagonal. (Assume that the screen is bright enough to see at this distance.) ?

Explanation / Answer

PART A:

From Rayleigh crtterion, we have

(theta_min) = (1.22(lambda))/D

where

theta_min = atan(281micrometers/1.3m)

So,

atan(281micrometers/1.3m)=(1.22(lambda))/D , Given Lambda = 550 nanometers,

D=(1.22(lambda)) /atan(281micrometers/1.3m)

on substituting, we get

D = 3.1 mm

PART:B:

The seperation between two pints on screen is given by 0.36 m,

By using Rayleigh criterion for resolution at which the two points are just resolved, we get the distance as 1670 m

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