The 775 nm and 1550 nm transmission peaks in the output filter cavity might fluctuate over short timescales, shorter than we'd expect from thermal fluctuations. One cause could be sound waves modulating the air, which has an index of refraction with wavelength dependence.

The optical path length (OPL) = L * n, where L is the length of the cavity ( which is 2.4 m) and n is the index of refraction.

\[ n = 1 + (n_0 - 1)\frac{\rho}{\rho_0} = 1 + (n_0 - 1)\frac{P}{P_0} \]

Where the variables with the subscript 0 are the nominal values. For 775 nm light, n_0 = 1.000275, while for 1550 nm light, n_0 = 1.000273, accoring to this website.

Thus, 

\[ n_{\text{rms}} = (n_0 - 1)\frac{P_{\text{rms}}}{P_0} \]

\[ P_{\text{rms}} = P_{\text{ref}} 10^{L_p / 20} \]

P_ref = 20 uPa

\[ OPL_{\text{rms}} =L(n_0 - 1)\frac{P_{\text{ref}} 10^{L_p / 20} }{P_0} \]

This formula agrees with this post, up to a small multiplicative factor of 1/n^2.

Let's assume a moderately loud L_p = 60 dB

775 nm OPL_rms = 1.32*10^-10 m

1550 nm OPL_rms = 1.31*10^-10 m

\[ OPL_{\text{rms, diff}} =L(\Delta n)\frac{P_{\text{ref}} 10^{L_p / 20} }{P_0} \]

So the difference in OPL_rms between the wavelengths is 1*10^-12 m = 1 pm.