Q. 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 dots can be resolved by the eye? [Take wavelength of light = 500 nm]
(a) 6m
(b) 3m
(c) 5m
(d) 1m
Ans : C
Sol: Limit of Resolution
$ \displaystyle \theta = \frac{1.22\lambda}{D} $
If d is the distance at which dots are just resolved then,
$ \displaystyle \theta = \frac{10^{-3}}{d} $
$\displaystyle \frac{10^{-3}}{d} = \frac{1.22\lambda}{D} $
$ \displaystyle d = \frac{10^{-3}\times D}{1.22\lambda} $
$\displaystyle d = \frac{10^{-3}\times 3\times 10^{-3}}{1.22\times 500\times 10^{-9}} $
d ≈ 5 m