Coherent sources and sustained interference of light
Understanding the conditions required for obtaining coherent sources and observing sustained interference patterns.
What is Coherent sources and sustained interference of light?
Two or more sources of waves that emit waves with the same frequency and a constant phase difference between them.
Key formula / rule: Phase difference and path difference
Key points
- Define coherent sources of light.
- State the conditions for sustained interference.
- Explain why independent sources are generally not coherent.
- Relate the concept of coherent sources to experimental setups like Young's double-slit experiment.
Common exam trap
Assuming any two light bulbs can act as coherent sources.
Definitions
- Term
Coherent Sources
- Meaning
Two or more sources of waves that emit waves with the same frequency and a constant phase difference between them.
- Term
Sustained Interference
- Meaning
An interference pattern that remains stationary and observable over time, requiring coherent sources.
- Term
Phase Difference
- Meaning
The difference in phase between two waves at a given point in space and time.
Learning objectives
Define coherent sources of light.
State the conditions for sustained interference.
Explain why independent sources are generally not coherent.
Relate the concept of coherent sources to experimental setups like Young's double-slit experiment.
Formulae
- Name
Phase difference and path difference
- Note
\Δ \φ is the phase difference, \λ is the wavelength, and \Δ x is the path difference.
- Expression
\Δ \φ = \frac{2 \π}{\λ} \Δ x
- Name
Condition for constructive interference
- Note
Leads to bright fringes.
- Expression
\Δ \φ = 2n\π \text{ or } \Δ x = n\λ \quad (n=0, 1, 2, ...)
- Name
Condition for destructive interference
- Note
Leads to dark fringes.
- Expression
\Δ \φ = (2n+1)\π \text{ or } \Δ x = (n+\frac{1}{2})\λ \quad (n=0, 1, 2, ...)
Prerequisites
Wave nature of light
Superposition principle
Phase and phase difference
Frequency and wavelength
Common mistakes
Assuming any two light bulbs can act as coherent sources.
Confusing constant phase difference with zero phase difference.
Not understanding that the intensity at points of constructive interference is not simply the sum of individual intensities due to the phase difference.
Keywords
Coherent sources
Sustained interference
Phase difference
Path difference
Young's double-slit
Superposition
Constructive interference
Destructive interference
Practice preview
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