First slide

Coherent sources and their importance in interference

Question

Consider two coherent point sources $(S_{1} and S_{2})$ separated by a small distance along a vertical line and two screens $P_{1} and P_{2}$ placed as shown in Figure. Which one of the choices represents the shapes of the interference fringes at the central regions on the screens?

Moderate

A

$Circular on P_{1} and hyperbolas on P_{2}$
B

$Circular on P_{1} and circular on P_{2}$
C

$Straight lines on P_{1} and hyperbolas on P_{2}$
D

$Straight lines on P_{1} and circular on P_{2}$

Solution

For any point on screen $P_{1}$ , the diagram is as shown below.

We can see for point $P$ and $P'$ the path difference would be same and hence they will have same intensity of light. On the $x - y$ plane, circumference of the circle (radius $y$ ) will also have same intensity ( $∵$ same path difference). Hence the shape will be circular.
For screen $P_{2}$ ,we will get hyperbola( from the knowledge of YDSE).
Therefore, the correct answer is (A).

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