# Chiral nematic liquid crystals - describing light diffraction

## Main Question or Discussion Point

So my book has an equation describing the wavelengths of light that are diffracted by a chiral nematic liquid crystal in terms of the refractive index (n), the pitch of the helix (p), and the angle (θ) with respect to the surface. The equation is this -

λ = np√((1-cos2θ)/n2)

If this isn't clear, inside the square root is (1-cos2θ) divided by n2. But isn't this whole expression the same as p*sinθ? I would think the top of the square root would equal sin2θ, then with the square root the n's would cancel. But this would mean that the wavelength doesn't depend on the diffraction index at all. Am I doing something dumb here?

Borek
Mentor
No idea about the theory behind, but if the equation is

$$\lambda = n p \sqrt{\frac {1-\cos^2(\theta)}{n^2}} = p \sqrt{1-\cos^2(\theta)}$$

you are right about n canceling.

(see our $\LaTeX$ FAQ for details on equation formatting, it comes handy in situations like this).