Edexcel A Level (IAL) Physics-2.7 Interference & Superposition of Waves- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -2.7 Interference & Superposition of Waves- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -2.7 Interference & Superposition of Waves- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
- know and understand what is meant by wavefront, coherence, path difference, superposition, interference and phase
Wavefront, Coherence, Path Difference, Superposition, Interference and Phase
This section explains the fundamental concepts used in wave optics and interference phenomena.
Wavefront
A wavefront is a surface (or line, in 2D diagrams) that joins points on a wave that are in the same phase.
- All points on a wavefront reach crests/troughs at the same time.
- Wavefronts are always perpendicular to the direction of wave propagation.
- Examples:
- Circular wavefronts (from a point source)
- Plane wavefronts (waves far from the source)
Coherence
Two sources are coherent if they have:
- the same frequency, and
- a constant phase difference
Coherence is essential for producing a stable interference pattern.
Path Difference
Path difference is the difference in the distances travelled by two waves from their respective sources before meeting at a point.
\( \Delta x = x_1 – x_2 \)
- Measured in metres (m).
- Determines whether waves interfere constructively or destructively.
Conditions:
- Constructive interference → \( \Delta x = n\lambda \)
- Destructive interference → \( \Delta x = (n+\tfrac{1}{2})\lambda \)
Superposition
Superposition is the principle that when two or more waves meet, the resultant displacement is the vector sum of the individual displacements.
- Waves pass through each other without being permanently changed.
- Can produce constructive and destructive interference.
Interference
Interference is the observable effect of superposition.
When two coherent waves overlap, they can produce:
- Constructive interference (in-phase overlap → larger amplitude)
- Destructive interference (out-of-phase overlap → cancellation)
Examples:
- Young’s double-slit fringes
- Thin-film interference
- Ripple tank patterns
Phase
Phase describes the position of a point within a wave cycle.
- Measured in radians or degrees.
- One complete cycle = \( 2\pi \) radians = \( 360^\circ \).
- Two points are in phase if they reach maximum displacement at the same time.
- Two points are out of phase if their peaks do not line up.
Phase difference:
\( \phi = \frac{2\pi}{\lambda} \Delta x \)
Example (Easy)
What condition is required for two sources to be coherent?
▶️ Answer / Explanation
- Same frequency
- Constant phase difference
Example (Medium)
Two waves arrive at a point with a path difference of \( \lambda/2 \). What type of interference occurs?
▶️ Answer / Explanation
\( \Delta x = \frac{\lambda}{2} = \left(n+\frac{1}{2}\right)\lambda \) → destructive interference.
Example (Hard)
Two sources produce waves with a phase difference of \( \pi/2 \). What is the corresponding path difference?
▶️ Answer / Explanation
Use the formula:
\( \phi = \frac{2\pi}{\lambda}\Delta x \)
Substitute \( \phi = \pi/2 \):
\[ \frac{\pi}{2} = \frac{2\pi}{\lambda}\Delta x \]
Rearrange:
\( \Delta x = \frac{\lambda}{4} \)
So the path difference = \( \lambda/4 \)