Question

Two coherent point sources $S_1$ and $S_2$ are separated by a small distance $d$ as shown. The fringes obtained on the screen will be

• A. points
• B. straight lines
• C. semi-circle
• D. concentric circles

Answer 1

The Correct Option is D

The problem involves the interference pattern created by two coherent point sources $S_1$ and $S_2$ separated by a small distance $d$. When these sources emit waves that meet at a screen, they produce an interference pattern. Let's analyze the nature of this pattern.

Concept of Interference: Interference patterns depend on the path difference of the waves reaching a particular point on the screen. Constructive interference occurs where the path difference is an integral multiple of the wavelength, creating bright fringes.

Analysis of Interference from Point Sources:

• When two point sources are very close together, the interference pattern typically forms due to differences in path length from each source to the screen.
• For small separations, the path difference varies circularly around the midpoint of the sources. This means points equidistant from the two sources (producing constructive interference) create concentric circular patterns.

Thus, in this configuration of two coherent point sources, the interference pattern formed on the screen will be concentric circles.

Let's justify why other given options are incorrect:

• Points: The interference cannot be isolated points on the screen because there are continuous regions of constructive and destructive interference.
• Straight lines: Straight line patterns are more typical in cases where there is a plane wave incidence, not point sources.
• Semi-circle: A semi-circular pattern could emerge if there were certain boundary conditions or obstructions, which is not specified here.

Given these explanations and the concept of interference from coherent sources, the interference pattern observed would be concentric circles, as indicated in the correct option.