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The human eye has an approximate angular...

The human eye has an approximate angular resolution of `phi=5.8xx10^(4)` rad and a typical photo printer prints a minimum of 300 dpi (dots per inch, 1 inch = 2.54 cm). At what minimal distance z should a printed page be held so that one does not see the individual dots.

Text Solution

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( `S_(1)` and `S_(2)` are two consecutive dots on the paper)
As shown in the figure, suppose images of two consecutive dots `S_(1)` and `S_(2)` (on he paper at distance Z from the eye) can be seen clear and just separated by an eye. Here distance `d_(m)` between `S_(2)` and `S_(2)` is called "linear limit of resolution" of an eye and angle `alpha_(min)=phi` is called "angular limit of resolution" of an eye.
Now as per the definition of measurement of angle in radian,
angle `=(arc)/("radius")`
`:.alpha_(min)=(d_(m))/(R)`
or `phi=(d_(m))/(Z)`
`:.Z=(d_(m))/(phi)`
`:.Z=(((2.54cm)/(300)))/(5.8xx10^(-4))`
`:.Z=(254)/(3xx5.8)=14.6cm`
If the paper is kept at a distance greater than 14.6 cm then images of `S_(1)` and `S_(2)` can not be seen clear and separated. Hence required minimum distance is Z = 14.6 cm.
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