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, `= 2.54 cm`). Aminimum distance 'z' should a printed page be held so that one doesnot see the indivdual dots is ______ .

Options

A. 17 cm
B. 12.5 cm
C. 14.5 cm
D. 16.3 cm

Answer

C

Explanation

The printer prints 300 dots per inch.
`therefore` The linear distance between two dots=d
`=(2.54)/(300)cm=0.84xx10^(-2)cm`
At a distance of z cm, this distance subtends an angle `phi`.
`because tanphi=phi=(d)/(z)`

`therefore z=(d)/(phi)=(0.84xx10^(-2))/(5.8xx10^(-4))=(84)/(5.8)=14.5cm`