Chiral nematic liquid crystals - describing light diffraction

[maxbashi]

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]

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).