Confused about interference pattern of waves

[toforfiltum]

Homework Statement

Homework Equations

dsinθ =nλ

The Attempt at a Solution

I don't understand why an interference pattern will only be observed along XY only. Why don't the waves intersect along RS. Does it have something to do with R being the midpoint of PQ?

 

[andrevdh]

The waves propagate outwards from P and Q, like two stones thrown in a pond.
The waves encounter each other at every point along the plane and interfere with
each other at each point. All along RS the interference will be constructive and
one would not observe a "pattern" there.

 

[toforfiltum]

The waves propagate outwards from P and Q, like two stones thrown in a pond.
The waves encounter each other at every point along the plane and interfere with
each other at each point. All along RS the interference will be constructive and
one would not observe a "pattern" there.

Oh, I see. How do you know that constructive interference occurs along RS?

 

[andrevdh]

The path length from P to a point on the line is the same as the path length
from Q to the same point on the line, so the path difference between the two
waves to travel to this point is zero. That means that they will arive in phase
with each other along the line RS so constructive interference will occur
between the two waves along the line.

 

[toforfiltum]

The path length from P to a point on the line is the same as the path length
from Q to the same point on the line, so the path difference between the two
waves to travel to this point is zero. That means that they will arive in phase
with each other along the line RS so constructive interference will occur
between the two waves along the line.

Ok, thanks!