A parallel beam of monochromatic light of wavelength `5000Å` is incident normally on a single narrow slit of width `0.001mm`. The light is focused by a convex lens on a screen placed on the focal plane. The first minimum will be formed for the angle of diffraction equal to

Options

A. `0^(@)`
B. `15^(@)`
C. `30^(@)`
D. `60^(@)`

Explanation

To solve the problem of finding the angle of diffraction for the first minimum in a single slit diffraction pattern, we will follow these steps:

### Step 1: Understand the given data
- Wavelength of light, \( \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \)
- Width of the slit, \( a = 0.001 \, \text{mm} = 0.001 \times 10^{-3} \, \text{m} = 1 \times 10^{-6} \, \text{m} \)

### Step 2: Use the diffraction formula
The condition for the first minimum in a single slit diffraction pattern is given by the formula:
\[ a \sin \theta = n \lambda \]
where \( n \) is the order of the minimum. For the first minimum, \( n = 1 \).

### Step 3: Substitute the values into the formula
Substituting \( n = 1 \) into the formula, we have:
\[ a \sin \theta = 1 \cdot \lambda \]
This simplifies to:
\[ \sin \theta = \frac{\lambda}{a} \]

### Step 4: Calculate \( \sin \theta \)
Now, substituting the values of \( \lambda \) and \( a \):
\[ \sin \theta = \frac{5 \times 10^{-7}}{1 \times 10^{-6}} = \frac{5}{10} = \frac{1}{2} \]

### Step 5: Find the angle \( \theta \)
To find \( \theta \), we need to determine the angle for which \( \sin \theta = \frac{1}{2} \). This occurs at:
\[ \theta = 30^\circ \]

### Conclusion
Thus, the angle of diffraction for the first minimum is:
\[ \theta = 30^\circ \]