Question

The aperture of the human eye is $2mm$. Assuming the mean wavelength of light to be $5000A^{°}$ , the angular limit of resolution of the eye is nearly

• A. $1$ minute
• B. $2$ minute
• C. $0.5$ minute
• D. $1.5$ minute

Answer 1

The correct option is A

$1$ minute

Step 1. Given data:

Aperture of the human eye = $2mm$

Mean wavelength of light = $5000A^{°}$

Step 2. Formula used:

Angular resolution is the ability of the eye to distinguish the smaller details of an object.

If the angular limit of resolution of the human eye is $R$ in radians, then

We know $R=\frac{1.55\lambda }{a}$

Where, $\lambda$= mean wavelength of light, $a$= aperture of the human eye,

Step 3. Calculations:

$R=\frac{1.55\times 5\times {10}^{-7}}{2\times {10}^{-3}}rad$

Now we will convert radians into minutes, which gives

$$\begin{gathered} R=\frac{1.55\times 5\times {10}^{-7}}{2\times {10}^{-3}}\times \frac{180}{\mathrm{\pi }}\times 60minute \\ =1minute \end{gathered}$$

Thus, the correct option is option A.