Two identical coherent sources of wavelength `lambda` are placed at `(100 lambda, 0)` and `(-50 lambda, 0)` along x-axis. The number of maxima and minima detected are ,respectively [include origin and `(5 lambda, 0)]`

Options

A. 51 and 50
B. 101 and 100
C. 49 and 50
D. 50 and 49

Explanation

To solve the problem, we need to determine the number of maxima and minima produced by the two coherent sources located at (100λ, 0) and (-50λ, 0) along the x-axis.

### Step-by-Step Solution:

1. **Identify the Positions of the Sources:**
The two coherent sources are located at:
- Source S1 at (100λ, 0)
- Source S2 at (-50λ, 0)

2. **Calculate the Distance Between the Sources (d):**
The distance \( d \) between the two sources can be calculated as:
\[ d = 100\lambda - (-50\lambda) = 100\lambda + 50\lambda = 150\lambda \]

3. **Determine the Path Difference for Maxima:**
The path difference \( \Delta x \) for maxima is given by:
\[ \Delta x = d = 150\lambda \]

4. **Calculate the Order of Maxima (n):**
The order of maxima \( n \) can be calculated using the formula:
\[ n = \frac{d}{\lambda} = \frac{150\lambda}{\lambda} = 150 \]

5. **Total Number of Maxima:**
The total number of maxima includes the central maximum and the maxima on both sides:
- There is 1 central maximum.
- There are 150 maxima on one side and 150 on the other side.
Therefore, the total number of maxima is:
\[ \text{Total Maxima} = 1 + 150 + 150 = 301 \]

6. **Total Number of Minima:**
The total number of minima can be calculated similarly:
- Between each pair of maxima, there is one minima.
- There are 150 maxima on one side and 150 on the other side, leading to 150 minima on each side.
Therefore, the total number of minima is:
\[ \text{Total Minima} = 150 + 150 = 300 \]

### Final Answer:
The total number of maxima is 301, and the total number of minima is 300.