Sulfur hexafluoride (SF6) is a high-density gas that has refractive index, ns = 1.8 at a specified pressure, temperature, and wavelength. Consider the retro-reflecting prism shown in Fig. 12.16, that is immersed in SF6. Light enters through a quarter-wave antireflective coating and then totally reflects from the back surfaces of the glass. In principle, the beam should experience zero loss at the design wavelength (P_out= P_in).

(a) Determine the minimum required value of the glass refractive index, n_g, so that the interior beam will totally reflect.

(b) Knowing n_g, find the required refractive index of the quarter-wave film, n_f.

(c) With the SF₆ gas evacuated from the chamber, and with the glass and film values as previously found, find the ratio, P_out/P_in. Assume very slight misalignment, so that the long beam path through the prism is not retraced by reflected waves.

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