Light of wavelength `5,000 Å` is normally illuminates a 0.2 mm wide slit. Calculate the angular spread between central maximum and first order maximum of the formed diffraction pattern.

Answer

To solve the problem of calculating the angular spread between the central maximum and the first-order maximum in a single-slit diffraction pattern, we can follow these steps:

### Step 1: Identify the given values
- Wavelength of light, \( \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \)
- Width of the slit, \( b = 0.2 \, \text{mm} = 0.2 \times 10^{-3} \, \text{m} = 2 \times 10^{-4} \, \text{m} \)

### Step 2: Use the formula for angular position of the first maximum
In single-slit diffraction, the condition for the first-order maximum is given by:
\[ \sin \theta = \frac{m \lambda}{b} \]
where \( m = 1 \) for the first maximum.

### Step 3: Substitute the values into the formula
Substituting \( m = 1 \), we have:
\[ \sin \theta = \frac{1 \times (5 \times 10^{-7})}{2 \times 10^{-4}} \]

### Step 4: Calculate \( \sin \theta \)
Calculating the right-hand side:
\[ \sin \theta = \frac{5 \times 10^{-7}}{2 \times 10^{-4}} = \frac{5}{2} \times 10^{-3} = 2.5 \times 10^{-3} \]

### Step 5: Approximate \( \theta \) for small angles
For small angles, \( \sin \theta \approx \theta \) (in radians). Therefore:
\[ \theta \approx 2.5 \times 10^{-3} \, \text{radians} \]

### Step 6: Conclusion
The angular spread between the central maximum and the first-order maximum is approximately:
\[ \theta \approx 2.5 \times 10^{-3} \, \text{radians} \]