Angular resolving power of human eye is

Options

A. `3.6xx10^(3)`rad
B. `3.6xx10^(2)`rad
C. `3.6xx10^(4)`rad
D. `3.6xx10^(6)`rad

Explanation

To find the angular resolving power of the human eye, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Angular Resolving Power**:
The angular resolving power (R) is defined as the reciprocal of the resolving limit (L). Mathematically, this can be expressed as:
\[ R = \frac{1}{L} \]

2. **Finding the Resolving Limit for Human Eye**:
The resolving limit for the human eye is given as \( \frac{1}{60} \) degrees. This means that the smallest angle that the human eye can resolve is \( \frac{1}{60} \) degrees.

3. **Converting Degrees to Radians**:
Since the options for the angular resolving power are given in radians, we need to convert \( \frac{1}{60} \) degrees into radians. The conversion formula from degrees to radians is:
\[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \]
Thus, we have:
\[ L = \frac{1}{60} \times \frac{\pi}{180} \]

4. **Calculating the Resolving Limit**:
Simplifying the above expression:
\[ L = \frac{\pi}{60 \times 180} = \frac{\pi}{10800} \]

5. **Calculating the Angular Resolving Power**:
Now, substituting the value of \( L \) back into the equation for \( R \):
\[ R = \frac{1}{L} = \frac{1}{\frac{\pi}{10800}} = \frac{10800}{\pi} \]

6. **Approximating the Value**:
Using the approximate value of \( \pi \approx 3.14 \):
\[ R \approx \frac{10800}{3.14} \approx 3435.7 \]
This can be rounded to \( 3.6 \times 10^3 \) radians.

7. **Final Answer**:
Therefore, the angular resolving power of the human eye is:
\[ R \approx 3.6 \times 10^3 \text{ radians} \]

### Conclusion:
The correct answer is option 1: \( 3.6 \times 10^3 \) radians.

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