Question

Two coherent point sources and are separated by a small distance ‘d’ as shown. The fringes obtained on the screen will be:

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

Answer 1

Hint: The wave front of a point source is spherical in nature and when this wave fronts from different sources interact with each other then an interference pattern is formed on the screen in front of the slits. When two such sources are placed as shown in the figure, then the interference occurring between them is such that the path difference is constant for the given angle at which the fringes are formed.

Complete answer:
We are given two coherent point sources and which are separated by a small distance ‘d’ as shown in the given figure.
In interference, the wave fronts of two light sources superimpose on each other to produce an interference pattern. As we know that the wave front of a point source is spherical in nature, when two such point sources are placed as shown in the diagram then interference between the light from these sources occurs in such a way that the spherical symmetry of the wave fronts is maintained. As a result, for a given angle with respect to slits at which the fringes are formed, the path difference remains constant. The locus of all such points is a circle. So, the interference pattern form in the given case consists of concentric circles.

Therefore, the correct answer is option C.

Note:
It should be noted that changing the position of the slits will change the interference pattern. When the slits are placed one above the other at equal distance from screen then the interference pattern formed consists of straight lines. We can also get elliptical and hyperbolic patterns depending on the position of the slits.