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