Question

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

• A. $5m$
• B. $1m$
• C. $6m$
• D. $3m$

Answer 1

The correct option is A $5m$

Resolution limit$=\frac{1.22\lambda }{D}$

(R.L)

where $\lambda =wavelength$

$D=$ daimeter of pupil of the eye

Then, according to question

$R.L=\frac{1.22\times 500nm}{3mm}=\frac{1.22\times 500\times {10}^{-9}}{3\times {10}^{-3}}$

Also, we know

$R.L=\frac{distanceb/wdots}{resolvingdistance}$

$\frac{1.22\times 500\times {10}^{-9}}{3\times {10}^{-9}}=\frac{1mm}{d}=\frac{1\times {10}^{-3}}{d}$

$d=\frac{{10}^{-3}\times 3\times {10}^{-3}}{1.22\times 5\times {10}^{-7}}$

$d=4.9180m$

$d\approx 5m$

Thus the maximum distance of dots can be

$5m$.