Two coherent point sources S 1 and S 2 are separated by a small distance ‘d’. The fringes obtained on the screen will be: (1) straight lines (2) semi-circles (3) concentric circles (4) points

When considering the interference pattern produced by two coherent point sources, the arrangement of the fringes on the screen is influenced by the geometry of the setup and the nature of the waves emitted by the sources. In this case, with two coherent point sources S1 and S2 separated by a small distance 'd', the resulting interference pattern will be a series of concentric circles.

Understanding Interference Patterns

Interference occurs when two or more waves overlap and combine. For coherent sources, which maintain a constant phase relationship, the resulting pattern can be predicted based on the path difference between the waves arriving at a point on the screen.

Why Concentric Circles?

When you have two point sources, each emitting waves that spread out in all directions, the waves will interfere constructively (resulting in bright fringes) and destructively (resulting in dark fringes) at various points on the screen. The key factors that determine the nature of the fringes are:

• Path Difference: The difference in distance traveled by the waves from each source to a point on the screen.
• Phase Relationship: The phase difference between the waves at that point, which depends on the path difference.

For points equidistant from both sources, the waves will arrive in phase, leading to constructive interference and bright fringes. Conversely, points where the path difference is an odd multiple of half wavelengths will experience destructive interference, resulting in dark fringes.

Visualizing the Pattern

Imagine placing two speakers (your point sources) a short distance apart and playing the same tone. The sound waves will radiate outward, and if you were to visualize the intensity of the sound at various points in the room, you would notice areas of loud sound (constructive interference) and areas of quieter sound (destructive interference). This pattern would manifest as concentric circles around the midpoint between the two speakers.

Summary of Options

Now, let’s evaluate the options provided:

• Straight lines: This would occur in a different setup, such as a single slit or a linear arrangement of sources.
• Semi-circles: This is not typical for two point sources; it might occur in specific geometrical arrangements.
• Concentric circles: This is the correct answer, as explained above.
• Points: This would imply discrete spots rather than a continuous pattern, which is not the case here.

In conclusion, the interference pattern produced by two coherent point sources separated by a small distance will indeed be concentric circles on the screen. This phenomenon beautifully illustrates the principles of wave interference and the behavior of sound or light waves in space.