The distance between consecutive maxima and minima is given by-

Options

A. `lambda//2`
B. `2lambda`
C. `lambda`
D. `lambda//4`

Answer

To solve the question about the distance between consecutive maxima and minima, we can follow these steps:

### Step 1: Understand the Conditions for Maxima and Minima
The condition for maxima in a wave interference pattern is given by the path difference being equal to \( n\lambda \), where \( n \) is an integer (0, 1, 2, ...). This means:
- For the first maxima (n=0), path difference = 0
- For the second maxima (n=1), path difference = \( \lambda \)
- For the third maxima (n=2), path difference = \( 2\lambda \)

The condition for minima is given by the path difference being equal to \( (2n-1)\frac{\lambda}{2} \):
- For the first minima (n=1), path difference = \( \frac{\lambda}{2} \)
- For the second minima (n=2), path difference = \( \frac{3\lambda}{2} \)
- For the third minima (n=3), path difference = \( \frac{5\lambda}{2} \)

### Step 2: Calculate the Distance Between Consecutive Maxima and Minima
To find the distance between consecutive maxima and minima, we can look at the path differences:

- The distance between the first maxima (0) and the first minima (\( \frac{\lambda}{2} \)):
\[ \text{Distance} = \frac{\lambda}{2} - 0 = \frac{\lambda}{2} \]

- The distance between the second maxima (\( \lambda \)) and the first minima (\( \frac{\lambda}{2} \)):
\[ \text{Distance} = \lambda - \frac{\lambda}{2} = \frac{\lambda}{2} \]

- The distance between the second minima (\( \frac{3\lambda}{2} \)) and the second maxima (\( \lambda \)):
\[ \text{Distance} = \frac{3\lambda}{2} - \lambda = \frac{\lambda}{2} \]

### Step 3: Conclusion
From the calculations above, we can see that the distance between consecutive maxima and minima is consistently \( \frac{\lambda}{2} \).

### Final Answer
The distance between consecutive maxima and minima is \( \frac{\lambda}{2} \).

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