Question

Aperture of the human eye is $2\text{mm}.$ Assuming the mean wavelength of light to be $5000\mathring{\text{A}}.$ The angular resolution limit of the eye is nearly

• A. $2\text{minute}$
• B. $1\text{minute}$
• C. $0.5\text{minute}$
• D. $1.5\text{minute}$

Answer 1

The correct option is B $1\text{minute}$

Given:
Aperture a $=2\text{mm};\lambda =5000\mathring{A}$

The angular limit of resolution of human eye is,

$R=\frac{1.22\lambda }{a}$

$\Rightarrow R=\frac{1.22\times 5\times {10}^{-7}}{2\times {10}^{-3}}=3.05\times {10}^{-4}\text{rad}$

$\therefore R=3.05\times {10}^{-4}\times \frac{{180}^{\circ }}{\pi }={0.0175}^{\circ }$

$\therefore R={0.0175}^{\circ }\times 60\text{minute}=1.05\text{minute}\approx 1\text{minute}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.