The diameter of the pupil of human eye is about `2 mm`. Human eye is most sensitive to the wavelength `555 nm`. Find the limit of resolution of human eye.

Options

A. 1.2 min
B. 2.4 min
C. 0.6 min
D. 0.3 min

Explanation

To find the limit of resolution of the human eye, we can follow these steps:

### Step 1: Understand the formula for the limit of resolution
The limit of resolution (Δθ) for a circular aperture (like the pupil of the human eye) is given by the formula:
\[ \Delta \theta = \frac{1.22 \lambda}{D} \]
where:
- \( \lambda \) is the wavelength of light,
- \( D \) is the diameter of the aperture.

### Step 2: Identify the given values
From the question:
- The diameter of the pupil \( D = 2 \, \text{mm} = 2 \times 10^{-3} \, \text{m} \)
- The wavelength \( \lambda = 555 \, \text{nm} = 555 \times 10^{-9} \, \text{m} \)

### Step 3: Substitute the values into the formula
Now substitute the values into the formula:
\[ \Delta \theta = \frac{1.22 \times (555 \times 10^{-9})}{2 \times 10^{-3}} \]

### Step 4: Calculate Δθ
Calculating the above expression:
\[ \Delta \theta = \frac{1.22 \times 555 \times 10^{-9}}{2 \times 10^{-3}} = \frac{678.1 \times 10^{-9}}{2 \times 10^{-3}} = \frac{678.1}{2} \times 10^{-6} = 339.05 \times 10^{-6} \, \text{radians} \]
\[ \Delta \theta \approx 3.39 \times 10^{-4} \, \text{radians} \]

### Step 5: Convert radians to degrees
To convert radians to degrees, use the conversion factor \( \frac{180}{\pi} \):
\[ \Delta \theta (\text{degrees}) = 3.39 \times 10^{-4} \times \frac{180}{\pi} \approx 0.0194 \, \text{degrees} \]

### Step 6: Convert degrees to minutes
Since 1 degree = 60 minutes, we convert degrees to minutes:
\[ \Delta \theta (\text{minutes}) = 0.0194 \times 60 \approx 1.164 \, \text{minutes} \approx 1.2 \, \text{minutes} \]

### Final Answer
The limit of resolution of the human eye is approximately **1.2 minutes**.

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