A Fabry-Perot cavity is formed by two identical partially reflecting mirrors separated by a distance d. Each mirror is lossless with reflection r and transmission t. In lecture, we calculated the transmitted intensity at steady state by summing all the transmitted rays, and get: IT = 10 X - *1 + F sin' 4 where lo is the incident intensity, F = 71-Ry; AR R = \\|2, and A is the phase acquired when a ray travels one round trip inside the cavity. (a) Sketch or plot ly as a function of A for R = 0.2, R = 0.5, and R = 0.9. Clearly indicate the maximum and minimum values of Ir, and values of A where the extrema occur. Calculate the coefficient of finesse F for each value of R. (b) Calculate the reflected intensity IR explicitly by summing all the reflected rays. Express your answer in terms of Jo, F and A, and show that Jo = IR + Ir. (c) By summing all the rays in between the two mirrors that are travelling to the right, or otherwise, show that the intensity of light circulating inside the cavity is: 1 - R circ = 10 X (1 - R)3 + 4Rsin' (d) Sketch or plot faire as a function of A for R = 0.2, R =0.5, and R = 0.9. Clearly indicate the maximum and minimum values