Interference | Notion

This topic is contained in pages $140-152$ of the textbook.

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Two waves are coherent if they have a constant phase relationship — same frequency and same wavelength.

For constructive interference to occur, two sources must be coherent and be an integer number of $\lambda$s apart, $\phi = 2n\pi$.

For destructive interference to occur, two sources must be coherent and be an odd number of half $\lambda$s apart, $\phi = (2n+1)\pi$.

The interference of waves from two point sources produces an interference pattern of constructive and destructive interference. This would cause a person walking from one source to another to hear the sound rising and falling as they moved through regions of constructive and destructive interference.

An interference pattern of bright spots can be produced by horizontal and vertical slits.

An optical path difference exists between two waves when they travel through different media as the change in refractive index causes the $\lambda$ of a wave to change.

→ The optical path length is equal to the product of the geometrical path length and the refractive index of the media, $opl=n\times gpl$.

→ The wavelength of light in another medium, e.g. glass, is shorter, relative to its wavelength in air. This can be derived using $n_{medium}=\frac{c}{v_{medium}}$.

$n_{medium}=\frac{f\lambda}{f\lambda_{medium}}$ ⇒ $n_{medium} \times\lambda_{medium} = \lambda$

$\lambda_{medium}=\frac{\lambda}{n_{medium}}$

The following relationship can be used to solve problems involving optical path difference, $opd$, geometrical path difference, $gpd$, and refractive index.

$$ opd=n \times gpd $$

Interference by division by amplitude occurs when light is split into two beams which interfere after reflection. The type of interference which occurs depends on the $opd$ of the two beams.