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.
- Consider 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:
$$
\text{Path difference} = n\lambda
$$
where $n$ is an integer (0, 1, 2, 3, ...).
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:
