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In non-relativistic systems both $E\sim k$ and $E\sim k^2$ are possible. Quadratic dispersion relations occur if $\langle 0|[Q_i,Q_j]|\rangle\neq 0$ for some of the generators. This occurs in a ferromagnet because rotational invariance is broken and $J_z$ has an expectation value. In terms of effective lagrangians the difference between ferromagnets and ...

First: I'd guess that by light dispersion you mean chromatic aberration. In general refocussing the light will not undo chromatic aberration, but it's possible to specifically design pairs of lenses to (mostly) eliminate it. These are called achromatic doublets. Second: yes, you need a bandpass filter. It's not possible to transmit everything below 600nm ...