<aside> 🌊 Diffraction is the bending and spreading of a wave whose wavelength is comparable to or greater than the slit width, or where $\lambda ≥ w$

As the size of the slit decreases, diffraction increases; with a shorter wavelength and no change in the size of opening, there is less diffraction

• Maximum width $w$ for noticeable diffraction occurs under the condition $\frac{\lambda}{w}= 1$ </aside>

• Interference occurs when two waves in the same medium meet

• Constructive interference occurs when the crest of one wave meets the crest of another wave

  • The resulting wave has an amplitude greater than that of each individual wave

• Destructive interference occurs when the crest of one wave meets the trough of another wave

  • The resulting wave has an amplitude less than that of each individual wave
  • Nodes are produced at locations where destructive interference occurs

• Waves with shorter wavelengths diffract less than waves with longer wavelengths

Two-Point-Source Interference

<aside> 🌊 A pair of identical point sources that are in phase produce a symmetrical pattern of constructive interference areas and nodal lines

</aside>

• The number of nodal lines in a given region will increase when the frequency of vibration of the sources increases, or when the wavelength decreases
• When the separation of the sources increases, the number of nodal lines also increases

Path length: distance from a point on the nodal line to source

The relationship that can be used to solve for an unknown variable in a two-point source interference pattern is $\triangle s =(n - \frac{1}{2})\lambda = |P_nS_1 - P_nS_2|$

• $P_n$ is any point on the $n$th nodal line
• $\triangle s$ is the path length difference
  • Path length difference can be calculated by finding the difference between the distances from the nodal line to each of the sources

To approximate the wavelength for an interference pattern when the point distance is much larger than the distance $d$

$\sin \theta_n = (n-\frac{1}{2})\frac{\lambda}{d}$

• $n$th nodal line is $\theta_n$
• Wavelength is $\lambda$
• Distance between the sources is $d$
• $x_n$ is the horizontal component of the distance from a point to the source
• $L$ is the actual length form the point to the source