An interference is observed due to two coherent sources `S_1` placed at origin and `S_2` placed at `(0, 3lambda, 0)`. Here, lambda is the wavelength of the sources. A detector D is moved along the positive x-axis. Find x-coordinates on the x-axis (excluding `x = 0 and x= oo`) where maximum intensity is observed.

Explanation

To find the x-coordinates on the x-axis where maximum intensity is observed due to the interference of two coherent sources \( S_1 \) (at the origin) and \( S_2 \) (at \( (0, 3\lambda, 0) \)), we will follow these steps:

### Step 1: Understand the setup
- The sources \( S_1 \) and \( S_2 \) are coherent and separated by a distance of \( 3\lambda \).
- A detector \( D \) is moved along the positive x-axis.

### Step 2: Determine the path difference
The path difference \( \Delta x \) between the waves arriving at the detector from \( S_1 \) and \( S_2 \) is given by:
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