Please answer in detail with all calculations and work.

A very narrow beam of unpolarized red light of intensity To is incident (at A) on a spherical water drop. The angle of incidence is 60. At A, some of the light is reflected and some enters the water drop. The refracted light reaches the surface of the drop at B where some of the light is reflected back into the water, and some emerges into the air. The light that is reflected back into the water reaches the surface of the drop at C where some of the light is reflected back into the drop, and some emerges into the air. Refractive index n of water for the red light is 1.331. Refractive index for air is 1. 600 B(a) What is the intensity of the light that refracts into the drop at A? What is the degree of polarization of the refracted light, i.e. how much of the intensity is spolarized and how much is ppolmized? (b) What is the intensity, and What is the degree of polarization of the light that reects at B? (c) What is the intensity, and what is the degree of polarization of the light that emerges into the air at C"? ((11) Let the angle of incidence at A be 91 and the angle of refraction at A be 92. Express ()5 (see gure) as a function of only 61 and 62. (e) Calculate the angle '35 in when 61 is 60. Do this for the red light and also for blue light (the index of refraction for blue light is 1.343). The speed of blue light in water is about 1% slower than that of red light. (f) For a given wavelength, there is one and only one value of 01 for which q is a maximum (qux). Prove that this is the case when (cos 6'1)2 = ('n,2 1) /3. Here n is the index of refraction. (g) Using the equation under (f), calculate the values of 91 for both the red and the blue light that give rise to maximum values for (b. Using your result under (d), calculate the maximum values for (b (each wavelength will have its own set of values for 61 and associated om\"). (h) In a world, farfar away, rain comes down as small drops of glass (with index of refraction of about 1.5). What is the maximum value of (,5 for these \"glassbows\"? Calculate for red light and compare the value with our rainbows. Remark: The 60 angle of incidence, is very close to the values you found in (g). Thus the value of qb as shown in the gure is also very close to your qux values in (g). The fact that gbmax is different for the red light than for the blue, is key in the formation of the rainbow