Interference of light waves and Young’s double slit experiment
Studying the phenomenon of interference of light and the experimental setup of Young's double-slit experiment.
What is Interference of light waves and Young’s double slit experiment?
Two sources of light are said to be coherent if they emit waves that have the same frequency and a constant phase difference.
Key formula / rule: Path difference for constructive interference
Key points
- Understand the phenomenon of interference of light.
- Explain the conditions for constructive and destructive interference.
- Describe the setup and working of Young's double-slit experiment.
- Derive the expression for fringe width.
Common exam trap
Confusing coherent and incoherent sources.
Definitions
- Term
Coherent sources
- Meaning
Two sources of light are said to be coherent if they emit waves that have the same frequency and a constant phase difference.
- Term
Interference
- Meaning
The phenomenon of superposition of two or more waves resulting in a redistribution of energy, leading to regions of maximum and minimum intensity.
- Term
Constructive interference
- Meaning
Superposition of waves where crests meet crests and troughs meet troughs, resulting in increased amplitude and intensity.
- Term
Destructive interference
- Meaning
Superposition of waves where crests meet troughs, resulting in decreased amplitude and intensity, potentially zero.
- Term
Fringe
- Meaning
An alternate bright or dark band observed in an interference or diffraction pattern.
- Term
Fringe width
- Meaning
The distance between the centers of two consecutive bright fringes or two consecutive dark fringes in an interference pattern.
Learning objectives
Understand the phenomenon of interference of light.
Explain the conditions for constructive and destructive interference.
Describe the setup and working of Young's double-slit experiment.
Derive the expression for fringe width.
Analyze the interference pattern observed on the screen.
Formulae
- Name
Path difference for constructive interference
- Note
n represents the order of the bright fringe.
- Expression
Δx = nλ, where n = 0, 1, 2, ...
- Name
Path difference for destructive interference
- Note
n represents the order of the dark fringe.
- Expression
Δx = (n + 1/2)λ, where n = 0, 1, 2, ...
- Name
Phase difference
- Note
Relates path difference to phase difference.
- Expression
Δφ = (2π/λ) * Δx
- Name
Fringe width
- Note
λ: wavelength, D: distance from slits to screen, d: distance between slits.
- Expression
β = λD/d
- Name
Intensity in interference
- Note
For equal amplitudes (I₁=I₂=I₀), I = 4I₀ cos²(Δφ/2). Max intensity = 4I₀, Min intensity = 0.
- Expression
I = I₁ + I₂ + 2√(I₁I₂) cos(Δφ)
Prerequisites
Wave nature of light
Huygens' principle
Diffraction
Superposition principle
Phase and path difference
Common mistakes
Confusing coherent and incoherent sources.
Incorrectly applying the conditions for constructive and destructive interference (e.g., using phase difference instead of path difference).
Forgetting the factor of 1/2 in the destructive interference path difference formula.
Assuming the central fringe is dark.
Keywords
Interference
Superposition
Coherent sources
Young's double slit experiment
Bright fringe
Dark fringe
Path difference
Phase difference
Fringe width
Monochromatic light
Practice preview
Two coherent sources of light are separated by a distance of 0.1 mm. They emit waves of wavelength 600 nm. The interference pattern is observed on a screen at a distance of 1 m from the sources. The position of the first…
medium
In Young's double-slit experiment, if the monochromatic source is replaced by a source of white light, then:…
medium
In Young's double-slit experiment, if the distance between the slits is halved and the distance between the slits and the screen is doubled, then the fringe width will:…
easy