A vitreous silica optical fiber of diameter 100m is used to send optical signals from a sensor

A vitreous silica optical fiber of diameter 100μm is used to send optical signals from a sensor placed deep inside a hydrogen chamber. The hydrogen is at a pressure of 20 bars. The mass diffusivity and solubility of the hydrogen in the glass fiber are D_AB = 2.88 x 10^-15 m²/s and S = 4.15 x 10^-3k mol/m³ ∙ bar, respectively. Hydrogen diffusion into the fiber is undesirable, since it changes the spectral transmissivity and refractive index of the glass and can lead to failure of the detection system.

(a) Determine the average hydrogen concentration in an uncoated optical fiber, C, after 100 hours of operation in the hydrogen environment. Determine the corresponding change in the refractive index, ∆_n, of the fiber. For vitreous silica, ∆_n = (1.6 x 10^-3 m³/k mol) x C.

(b) Determine the average hydrogen concentration and change in refractive index after 1 hour and 10 hours of operation in the hydrogen environment.