Interference and Diffraction

## Definitions and General Principles

**Phase:** Position within a points cycle of oscillation on a wave (° or c)

**Path difference:** The difference in the distance travelled by two coherent waves from different sources (m)

**Interference:** The **superposition** of two or more waves

* **Constructive** interference occurs when the original waves add to give a resultant wave with a **greater** displacement (amplitude) than the original waves
	+ At a path difference of **nλ**
	+ **In phase** - At a phase difference of **2π** (causing maximum amplitudes/bright fringes/etc)
* **Destructive** interference occurs when the original waves add to give a resultant wave with a **smaller** displacement (amplitude) than the original waves (ie the waves cancel)
	+ At a path difference of **(n + 1/2)λ**
	+ **In Antiphase** - At a phase difference of **π**, half a cycle out of phase with another wave (producing minimum amplitudes/dark fringes/etc)

Maximum amplitude occurs at P if:  S2P - S1P = nλ

Minimum amplitude occurs at P if: S2P - S1P = (n + 1/2)λ

**Diffraction:** **Spreading** out of a wave as it passes **through** a **gap** (aperture), or **around** an **obstacle**

* Maximum diffraction occurs when the **gap = λ**
* When the gap > λ, **little** diffraction occurs
* When the gap < λ, diffraction occurs with **low intensity** (most of the wave is reflected)
* As the wave spreads out, the intensity is weakened

## Huygens' Principle & Single Slit Interference

**Every point** on a wavefront is a **point source** that **spreads** out spherically; the new wavefront is the surface that is tangential to these.

If a wave passes through a single slit (aperture), it will **diffract**.

There will be a **pattern** produced (due to Huygens' principle), of a **central bright fringe**, and **alternating** dark and bright fringes **either side**, which can be shown as **intensity** on a graph.

How much the pattern is spread depends on how the **wavelength** **compares** to the **slit width**, longer wavelengths will produce wider diffraction patterns.

Huygens' principle can also be used to demonstrate diffraction around obstacles/objects.

## Young's Double Slit & Diffraction gratings

For multiple slits, a **coherent** source must be used. This can be achieved by:

* Passing the source through a **single slit** first
* Ensuring the slits are **closely spaced** enough that the source can fit over all of them
* **Connecting** the sources (ie for speakers to the same oscillator)

An **interference pattern** will be produced, as before an **intensity graph** can be plotted from this. The more slits you add (after 2 slits) won't affect the pattern of the bright and dark spots.

**Increasing** the number of slits increases the **intensity**, and **decreases** the **width** of the **bright** spots (maximum amplitude).

nλ = dsinθ

* n = order of the fringe
* d = slit spacing
* θ = angle between zero and nth order (**RADIANS**)

If given the number of slits per metre (N), the slit spacing (d) = 1/N

## Electron diffraction

* Electrons **interact** with the **spaces** between the **atoms** in graphite
* **Diffraction** patterns and interference are observed
* Atom spacing ≈ λ
* Diffraction and interference are **wave behaviours**
* Therefore electrons show wave like properties
* **Slower** electrons give **wider** spaced rings