Flashback 1: Physics Class
Wave interference touches our lives in many ways.
Diffraction reveals the reciprocal perspective of waves, where small becomes big (and big small)!
Low angle diffraction holds lattice spacing d times scattered distance g to a camera constant equal to wavelength ? times camera length L, i. e. g d = ? L.
Ask students about ways they encounter wave interference in their lives. Examples that come up include the bathtub and surfing, the tuning of musical instruments (a time-domain glimpse into reciprocal space), feedback in driven oscillators like cars pulling trailers and collapsing bridges, the stability of electron states around atoms, quantum tunneling, Heisenberg uncertainty, and even the Feynman propagator that moves us into the future!
Also get them to help with derivation of the main equation (which incidentally works well for many kinds of small angle diffraction, including the Bragg kind as long as we recognize that the Bragg angle is defined as half the scattering angle). Although the equation as written only works for small angles (I.e. when theta in radians is essentially the same as its tangent and sine), the basic reciprocal relationship generalizes nicely in 3D to the Ewald sphere construction familiar to diffractionists, in quantum mechanics to the Fourier relationship between position and momentum, and in space-time to the relationship between vectors and one-forms.
Caution: In the expanded contents frame, the wavelength lamda may appear as a question mark (?) in the HTML code.