A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is

Options

A. 0
B. `(pi)/(2)`
C. `pi`
D. `2pi`

Explanation

To solve the problem, we need to determine the phase difference between the rays coming from the two edges of a narrow slit at the first minimum of the diffraction pattern.

### Step-by-Step Solution:

1. **Understand the Setup**: A parallel monochromatic beam of light is incident normally on a narrow slit. When light passes through the slit, it diffracts and creates a pattern on a screen.

2. **Identify the Condition for Minima**: The first minimum in the diffraction pattern occurs when the path difference between the light rays coming from the two edges of the slit is equal to one wavelength (λ). This is a fundamental condition for destructive interference.

3. **Path Difference at First Minimum**: At the first minimum, the path difference (Δx) between the rays from the two edges of the slit is given by:
\[ \Delta x = \lambda \]

4. **Relate Path Difference to Phase Difference**: The phase difference (Δφ) can be calculated using the formula:
\[ \Delta \phi = \frac{2\pi}{\lambda} \Delta x \]
where Δx is the path difference.

5. **Substituting the Path Difference**: Since we know that Δx = λ at the first minimum, we can substitute this into the equation:
\[ \Delta \phi = \frac{2\pi}{\lambda} \cdot \lambda \]

6. **Simplifying the Expression**: The λ in the numerator and denominator cancels out:
\[ \Delta \phi = 2\pi \]

7. **Conclusion**: Therefore, at the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is:
\[ \Delta \phi = 2\pi \]

### Final Answer:
The phase difference between the rays coming from the two edges of the slit at the first minimum of the diffraction pattern is \(2\pi\).

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