Question

Assuming human pupil to have a radius of $0.25\text{cm}$ and a comfortable viewing distance of $25\text{cm}$, the minimum separation between two objects that human eye can resolve at $500\text{nm}$ wavelength is

• A. $100\mu \text{m}$
• B. $300\mu \text{m}$
• C. $1\mu \text{m}$
• D. $30\mu \text{m}$

Answer 1

The correct option is D $30\mu \text{m}$


The limit of resolution is given by,

$d=\frac{1.22\lambda }{2\mu \sin \theta }$

As $\theta$ is very small,

$sin\theta \approx \theta =\frac{0.25}{25}=\frac{1}{100}$

$\Rightarrow d=\frac{1.22\times 500\times {10}^{-9}}{2\times 1\times \left(\frac{1}{100}\right)}$

$\Rightarrow d=3.05\times {10}^{-5}\text{m}=30.5\mu \text{m}$

$\therefore d\approx 30\mu \text{m}$

Hence, option $\left(\text{D}\right)$ is correct.