In Young's double slit experiment, The locus of the point P lying in a plane with a constant path difference between two interfering waves is

Options

A. a hyperbola
B. a straight line
C. an ellipse
D. a parabola

Explanation

To solve the question regarding the locus of a point P lying in a plane with a constant path difference between two interfering waves in Young's double slit experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Path Difference**: In Young's double slit experiment, when two waves emanate from two slits, they can interfere with each other. The path difference (\( \Delta x \)) between the two waves at any point P on the screen is crucial for determining the type of interference (constructive or destructive).

2. **Constant Path Difference**: The question specifies that the path difference is constant. This means we are looking for the locus of points where the path difference between the two waves remains the same, say \( \Delta x = d \).

3. **Geometric Interpretation**: The locus of points that maintain a constant path difference from two fixed points (the slits) can be visualized geometrically. If we consider the two slits as foci of a conic section, the points that have a constant path difference from these two points will form a specific curve.

4. **Identifying the Curve**: The locus of points that have a constant path difference from two fixed points is known to be a hyperbola. This is because, for a hyperbola, the difference in distances from any point on the hyperbola to the two foci is constant.

5. **Conclusion**: Therefore, the locus of the point P lying in a plane with a constant path difference between two interfering waves in Young's double slit experiment is a **hyperbola**.

### Final Answer:
The locus of the point P lying in a plane with a constant path difference between two interfering waves is a **hyperbola**.

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