How does the specific rotation of a crystal depend on temperature as well as wavelength of light used? I understand that the specific rotation of a substance depends inversely on the concentration of the solution and the length. I wish to know the exact nature of its dependence on temperature as well as the wavelength of light used.
 A: The specific rotation $[\alpha]_\lambda^T$ for a pure material (i.e. not a solution, but a pure solid, liquid, or gas) at a temperature $T$ and wavelength $\lambda$, given an observed optical rotation $\alpha$ under those conditions, a path length $l$, and density $\rho$, is given by
$$[\alpha]_\lambda^T=\frac{\alpha}{l\rho}$$
As you can see, the density of the material affects the specific rotation. The density of a material is itself affected by the temperature: thermal expansion changes the volume of the material (for small changes in temperature) according to:
$$\Delta V=\alpha_V V\Delta T$$
where $\alpha_V$ is the coefficient of bulk thermal expansion. Therefore, thermal expansion changes the specific rotation (there may be other processes that change the measured optical rotation $\alpha$ as a function of temperature; these factors are likely highly material-dependent and will not be discussed here).
Its dependence on the wavelength is quite complicated, as it essentially depends on the particular energy bands available inside a crystal, and as such there isn't really a general form for the dependence on wavelength; a summary of the much simpler case of a solution of molecules (not an interconnected network of ions) can be found here: https://chemistry.stackexchange.com/questions/73665/dependence-of-the-angle-of-rotation-on-the-wavelength-of-plane-polarized-light. Even for that case, it requires that you know the energy of all of the electronic states of the molecule. 
