Light of wavelength `589.3nm` is incident normally on the slit of width `0.1mm`. What will be the angular width of the central diffraction maximum at a distance of `1m` from the slit?

Options

A. `0.68^(@)`
B. `0.34^(@)`
C. `2.05^(@)`
D. None of these

Explanation

To solve the problem of finding the angular width of the central diffraction maximum for light of wavelength `589.3 nm` incident on a slit of width `0.1 mm`, we can follow these steps:

### Step 1: Convert the given values to SI units
- Wavelength \( \lambda = 589.3 \, \text{nm} = 589.3 \times 10^{-9} \, \text{m} \)
- Slit width \( D = 0.1 \, \text{mm} = 0.1 \times 10^{-3} \, \text{m} = 1 \times 10^{-4} \, \text{m} \)
- Distance from the slit \( L = 1 \, \text{m} \)

### Step 2: Use the formula for angular width of the central maximum
The angular width \( \theta \) of the central maximum in a single-slit diffraction pattern can be approximated using the formula:
\[ \theta \approx \frac{\lambda}{D} \]

### Step 3: Substitute the values into the formula
Substituting the values of \( \lambda \) and \( D \):
\[ \theta \approx \frac{589.3 \times 10^{-9} \, \text{m}}{1 \times 10^{-4} \, \text{m}} \]

### Step 4: Calculate \( \theta \)
Calculating the above expression:
\[ \theta \approx 5.893 \times 10^{-3} \, \text{radians} \]

### Step 5: Convert radians to degrees
To convert radians to degrees, use the conversion factor \( \frac{180}{\pi} \):
\[ \theta \approx 5.893 \times 10^{-3} \times \frac{180}{\pi} \approx 0.337 \, \text{degrees} \]

### Step 6: Final answer
Thus, the angular width of the central diffraction maximum is approximately:
\[ \theta \approx 0.34 \, \text{degrees} \]

### Summary
The angular width of the central diffraction maximum is \( \theta \approx 0.34 \, \text{degrees} \).

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