Two point white dots are 1mm apart on a black paper. They are viewed by eye of pupil diameter 3mm. Approximately, what is the maximum distance at which these dits can be resolved by the eye? [Take wavelelngth of light =500nm]

Options

A. `1 m`
B. `5 m`
C. `3 m`
D. `6 m`

Answer

B

Explanation

Limit of resolution eye
`= theta = (1.22 lambda)/(D)`
`= (1.22 xx 5 xx 10^(-7))/(3 xx 10^(-3)) = 2.03 xx 10^(-4) rad`
If `x` is the minimum distance at width dots are just resolved, then
`theta = (1 mm)/(x) = (10^(-3))/(x) = 2.03 xx 10^(-4)`
`x = (10^(-3))/(2.03 xx 10^(-4)) = 5 m`