In a single slit diffraction experiment, first minimum for a light of wavelength 540 nm coincides with the first maximum of another wavelength `lamda'`. Then `lamda'` is

Options

A. `3600Å`
B. `2700Å`
C. `4800Å`
D. `5200Å`

Explanation

To solve the problem, we need to understand the relationship between the wavelengths of light in a single slit diffraction experiment. The first minimum of one wavelength coincides with the first maximum of another wavelength.

### Step-by-Step Solution:

1. **Understanding the Condition for Minima and Maxima**:
- In a single slit diffraction pattern, the position of the minima is given by the formula:
\[ a \sin \theta = m \lambda \]
where \( m \) is the order of the minimum (for the first minimum, \( m = 1 \)), \( a \) is the width of the slit, and \( \lambda \) is the wavelength of light.
- The position of the maxima can be approximated (for small angles) by:
\[ y = \frac{n \lambda D}{a} \]
where \( n \) is the order of the maximum.

2. **Setting Up the Given Condition**:
- The first minimum for the wavelength \( \lambda_1 = 540 \, \text{nm} \) coincides with the first maximum for another wavelength \( \lambda' \).
- For the first minimum:
\[ a \sin \theta = \lambda_1 \quad \text{(for } m = 1\text{)} \]
- For the first maximum:
\[ y = \frac{n \lambda' D}{a} \quad \text{(for } n = 1\text{)} \]

3. **Relating the Two Conditions**:
- Since the first minimum coincides with the first maximum, we can equate the path differences:
\[ \frac{\lambda_1}{2} = \lambda' \]
- This is because the first minimum occurs at a path difference of \( \frac{\lambda_1}{2} \) while the first maximum occurs at a path difference of \( \lambda' \).

4. **Calculating the Wavelength \( \lambda' \)**:
- Substituting \( \lambda_1 = 540 \, \text{nm} \):
\[ \lambda' = \frac{540 \, \text{nm}}{2} = 270 \, \text{nm} \]

5. **Converting to Angstroms**:
- To convert \( \lambda' \) to angstroms:
\[ \lambda' = 270 \, \text{nm} = 2700 \, \text{angstroms} \]

### Final Answer:
The wavelength \( \lambda' \) is \( 270 \, \text{nm} \) or \( 2700 \, \text{angstroms} \).

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