Problem 3 Show that the free spectral range of an etalon with cavity thickness d, cavity...

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Problem 3 Show that the free spectral range of an etalon with cavity thickness d, cavity index of refraction n and intra-cavity angle 02 in dependence on the vacuum wavelength can be approximated as AFSR = 2f 2nd cos 02 Hint: Find first the general relationship between small wavelength and small frequency intervals (A and Av, respectively). Problem 4 Determine whether or not the following mirror cavities are stable and show all of these cavities geometry on the stability diagram. = = R2 = 0.9 m, separation of mirrors d 2.5 m; (a) Mirror radii of curvature R (b) R = 2 m, R2 = 3 m, d (c) R = 3 m, R2 = 5 m, d (d) R = R2 = 0.5 m, d = = 4 m; 0.5 m. - 1 m Problem 3 Show that the free spectral range of an etalon with cavity thickness d, cavity index of refraction n and intra-cavity angle 02 in dependence on the vacuum wavelength can be approximated as AFSR = 2f 2nd cos 02 Hint: Find first the general relationship between small wavelength and small frequency intervals (A and Av, respectively). Problem 4 Determine whether or not the following mirror cavities are stable and show all of these cavities geometry on the stability diagram. = = R2 = 0.9 m, separation of mirrors d 2.5 m; (a) Mirror radii of curvature R (b) R = 2 m, R2 = 3 m, d (c) R = 3 m, R2 = 5 m, d (d) R = R2 = 0.5 m, d = = 4 m; 0.5 m. - 1 m