How to show that the Airy function is Lorentzian

Question

The Airy function used to describe the reflected/transmitted intensity of a Fabry-Perot interferometer has the general form:

$$\frac{F\sin^{2}\left(\theta\right)}{1+F\sin^{2}\left(\theta\right)},$$

where $F$ is a constant known as the Finesse.

What would be a simple way to show that the dips in this function have a Lorentzian shape?

Any suggestions would be greatly appreciated.

P. S. Here is a plot I made that shows the dips that occur in the Airy function described above:

Answer 1

If the reflection is $$R=\frac{F\sin^2\theta}{1+F\sin^2\theta}$$ then the transmitted is $$T=1-\frac{F\sin^2\theta}{1+F\sin^2\theta}=\frac{1+F\sin^2-F\sin^2\theta}{1+F\sin^2\theta}=\frac{1}{1+F\sin^2\theta}=\frac 1F\frac{1}{\sqrt{\frac 1F}^2+\sin^2\theta}$$