Find the ratio of intensities at the two points `X and Y` on a screen in Young's double slit experiment, where waves from the two source `S_(1) and S_(2)` have path difference of zero, and `lambda//4` respectively.

Explanation

To solve the problem of finding the ratio of intensities at points X and Y in Young's double slit experiment, where the path differences are 0 and λ/4 respectively, we can follow these steps:

### Step 1: Define the Amplitudes
Let the amplitude of the wave from source S1 be \( A \) and the amplitude of the wave from source S2 be \( B \).

### Step 2: Calculate Intensity at Point X (Path Difference = 0)
When the path difference is 0, the waves from both sources S1 and S2 will be in phase. The resultant amplitude \( R \) at point X can be calculated as:
\[
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