(50 points) In the previous cumulative assignment, (some of) you calculated the transmission and internal intensity of the Fabry-Perot etalon. This question will have the same setup as that one, but now we will be using the reflection. For this question, you will be designing a Gires-Tournois interferometer (GTI) mirror, which is a specially made dispersion compensating mirror. Design the mirror as follows: you have a very thin piece of glass with index of refraction n of thickness L that is contacted to a highly reflecting mirror, R2=100%. (a) Sketch this setup and calculate the reflectivity (as in the field reflection amplitude and phase) of this mirror. Show that this reflectivity is rT()=1r1e2ir1+e2i where =cwnL and r1 is the Fresnel reflectivity given by the material index. (b) Show that the reflection coefficient RT=rT2 is unity for all frequencies or lengths. You can do this either analytically or numerically. (c) Now find the resulting phase imparted by this mirror. To do this analytically, you need to note that rT=rTei where is the total phase of the mirror (no, it's not ). Or you can do this numerically, which you can do in Python using the np.unwrap and np.angle functions. Read the documentation on how to use these functions