Interference and Young’s Double-Slit Experiment
The Principle of Superposition
When two or more waves overlap, the total displacement at any point is the sum of the individual displacements of each wave.
This is called the principle of superposition.
Note
The principle of superposition applies to all types of waves, including sound, light, and water waves.
Constructive and Destructive Interference
When waves overlap, they can interfere with each other in two main ways:
- Constructive Interference:
- Occurs when waves are in phase (e.g., crest meets crest).
- The resulting wave has a larger amplitude than the individual waves.
- Destructive Interference:
- Occurs when waves are out of phase (e.g., crest meets trough).
- The resulting wave has a smaller amplitude, and they can even cancel each other out completely.
Example
Imagine two water waves meeting in a pond.
- If their crests align, the water rises higher (constructive interference).
- If a crest meets a trough, the water becomes flat (destructive interference).
Path Difference and Interference
The type of interference depends on the path difference between the waves.
Path difference
Path difference is the difference in distance traveled by the waves from their sources to the point of overlap.
Constructive Interference
Constructive interference occurs when the path difference is an integer multiple of the wavelength:
where
Example
If two waves travel distances of 3λ and 4λ, the path difference is 1λ. Since this is an integer multiple of λ, the waves interfere constructively.
Destructive Interference
Destructive interference occurs when the path difference is a half-integer multiple of the wavelength:
Example
If two waves travel distances of 3.5λ and 4λ, the path difference is 0.5λ. Since this is a half-integer multiple of λ, the waves interfere destructively.
Tip
To determine the type of interference, calculate the path difference and compare it to the wavelength.
Young’s Double-Slit Experiment
Young’s double-slit experiment demonstrated the wave nature of light by showing an interference pattern of bright and dark fringes on a screen.
How It Works
- Light Source: A coherent light source (e.g., laser) illuminates two narrow, parallel slits.
- Diffraction: Light waves passing through the slits spread out and overlap.
- Interference: The overlapping waves create an interference pattern on a screen, with alternating bright and dark fringes.
Note
The light waves from the two slits arecoherent, meaning they have a constant phase relationship. This is essential for a stable interference pattern.
Fringe Spacing
Fringe spacing
Fringe spacing refers to the distance between adjacent bright or dark fringes in an interference pattern, typically observed in double-slit experiments or diffraction patterns.
The spacing between adjacent bright or dark fringes is determined by the formula:
where:
Tip
Fringe spacing increases with longer wavelengths, larger distances to the screen, and smaller slit separations.
Fringe spacing
In a double-slit experiment, light with a wavelength of 600 nm is used. The slits are 0.2 mm apart, and the screen is 2 m away.
What is the fringe spacing?
Solution
Using the formula:
Common Mistake
Don’t confuse path difference with phase difference.
Path difference is measured in terms of wavelength, while phase difference is measured in degrees or radians.
Reflection and Self-Assessment
Theory of Knowledge
How did Young’s experiment influence the scientific community’s understanding of light? What does this tell us about the role of evidence in shaping scientific theories?
Self review
- What is the path difference for constructive interference?
- How does fringe spacing change if the slit separation is doubled?
- Why is coherence important in Young’s experiment?
Understanding interference and Young’s experiment reveals the wave nature of light and the power of superposition.
