Here is a fiber thermometer with a Fabry-Pérot cavity (FP) placed at the extremity of the fiber as shown on the Figure below. The cavity's mirrors are supposed to all have the same reflection coefficient and to be insensitive to temperature's variations.
If we assume that the FP cavity is filled up with a material whose index is called n and that the cavity length is L, define the phase difference inserted in the cavity.
What impact has a variation of temperature on the answer of the FP?
How does the finesse vary according to the refractive index of the liquid?