Confused about interference pattern of waves

• toforfiltum
In summary, when two waves propagate outwards from points P and Q, they encounter each other at every point along the plane and interfere with each other. Due to the path length being the same from P and Q to any point on the line RS, the waves arrive in phase and result in constructive interference along the line. This explains why an interference pattern is only observed along XY and not RS.
toforfiltum

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?

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.

andrevdh said:
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?

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.

andrevdh said:
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!

1. What is an interference pattern?

An interference pattern is a pattern that is created when two or more waves interact with each other. This interaction causes the waves to combine and either amplify or cancel each other out, resulting in a pattern of alternating bright and dark spots.

2. How does interference occur?

Interference occurs when two or more waves meet at the same point in space. Depending on the phase difference between the waves, they can either constructively interfere (amplify each other) or destructively interfere (cancel each other out).

3. What factors affect interference patterns?

The factors that affect interference patterns include the wavelength of the waves, the distance between the sources of the waves, and the phase difference between the waves. Other factors such as the medium through which the waves are travelling can also have an impact.

4. What is the difference between constructive and destructive interference?

Constructive interference occurs when two waves meet in phase, meaning their peaks and troughs align and they amplify each other. Destructive interference occurs when two waves meet out of phase, meaning their peaks and troughs are opposite and they cancel each other out.

5. How are interference patterns used in science?

Interference patterns are used in many scientific fields, including optics, acoustics, and quantum mechanics. They can be used to study and understand the properties of waves, as well as to create new technologies such as interferometers and diffraction grating.

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