14.8 — Double-Slit Interference and Diffraction Gratings

As we learned in 14.7 — Diffraction, diffraction occurs when waves spread around the edges of an obstacle or through an opening, and then interferences with itself. it occurs for both sound waves and light waves. When a wave diffracts, the obstacle essentially acts as a new source of waves.

Here are some quick facts about sound waves and all electromagnetic waves:

Sound Waves	EM Waves
Longitudinal	Transverse
340m/s in air	300,000,000m/s in air
Can’t be polarized	Can be polarized
Interference effects	Interference effects
In double-slit interference,

• a greater wavelength will result in widely-spaced maxima
• a greater distance to the screen will result in widely-spaced maxima
• a greater spacing between openings will result in closely-spaced maxima

Continuing on the diagram in 14.7 — Diffraction, we have the following illustration and the derived formula:

We can manipulate the small angle equation to fit into $y=mx+b$ by assuming $mL$ is the x-value. When we’re looking at the first dark spot ($m=1$), the x-axis will simply represent $L$ which is the distance to the screen.