Interference & Diffraction Reference Cheat Sheet

Key Facts

• Constructive interference occurs when the path difference is $\Delta L = m\lambda$, where $m = 0, 1, 2, \ldots$.
• Destructive interference for two coherent sources occurs when the path difference is $\Delta L = \left(m + \frac{1}{2}\right)\lambda$.
• For a double slit, bright fringes satisfy $d\sin\theta = m\lambda$, where $d$ is slit spacing and $m$ is the order number.
• For a double slit at small angles, fringe spacing on a screen is $\Delta y = \frac{\lambda L}{d}$.
• For a single slit, dark minima satisfy $a\sin\theta = m\lambda$, where $a$ is slit width and $m = 1, 2, 3, \ldots$.
• For a diffraction grating, principal maxima satisfy $d\sin\theta = m\lambda$, where $d = \frac{1}{N}$ if $N$ is the number of lines per unit length.
• Longer wavelengths spread out more, so increasing $\lambda$ increases fringe spacing and diffraction angle.
• Coherent waves have a constant phase relationship, which is required for a stable interference pattern.

Vocabulary

Interference

Interference is the combining of two or more waves to form a new wave pattern with larger or smaller amplitudes.

Constructive Interference

Constructive interference occurs when waves meet in phase and their amplitudes add.

Destructive Interference

Destructive interference occurs when waves meet out of phase and their amplitudes partially or completely cancel.

Path Difference

Path difference is the difference in distance traveled by two waves before they meet, often written as $\Delta L$.

Diffraction

Diffraction is the bending and spreading of waves as they pass through an opening or around an obstacle.

Diffraction Grating

A diffraction grating is a surface with many closely spaced slits or lines that produces sharp interference maxima.