The diameter of human eye lens is `2 mm`. What should be the minimum separation between two points situated at `50 m` from eye, to resolve tham. Take wavelength of light `= 5000 Å`.

Options

A. 2.32 m
B. 4.28 mm
C. 1.525 cm
D. 12.48 cm

Explanation

To solve the problem of finding the minimum separation between two points that can be resolved by the human eye, we can use the formula derived from the Rayleigh criterion for resolution. The steps are as follows:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Diameter of the eye lens (d) = 2 mm = 2 × 10^(-3) m
- Distance to the points (L) = 50 m
- Wavelength of light (λ) = 5000 Å = 5000 × 10^(-10) m = 5 × 10^(-7) m

2. **Use the Rayleigh Criterion**:
The minimum angular resolution (θ) can be approximated using the formula:
\[ \sin \theta \approx \theta \approx \frac{1.22 \lambda}{d} \]

3. **Calculate θ**:
Substitute the values of λ and d into the formula:
\[ \theta \approx \frac{1.22 \times 5 \times 10^{-7}}{2 \times 10^{-3}} \]

4. **Perform the Calculation**:
\[ \theta \approx \frac{1.22 \times 5}{2} \times 10^{-4} = \frac{6.1}{2} \times 10^{-4} = 3.05 \times 10^{-4} \text{ radians} \]

5. **Find the Minimum Separation (d)**:
The minimum separation (s) between two points at distance L can be calculated using:
\[ s = L \cdot \theta \]
Substitute L and θ:
\[ s = 50 \cdot 3.05 \times 10^{-4} \]

6. **Perform the Final Calculation**:
\[ s = 50 \times 3.05 \times 10^{-4} = 1.525 \times 10^{-2} \text{ m} = 1.525 \text{ cm} \]

### Final Answer:
The minimum separation between the two points that can be resolved is **1.525 cm**.