Posted: May 20th, 2023

solar observations, physics homework help

Question description

In several of the problems below, you will need to estimate the visible-light brightness of the off-limbcorona. Feel free to use the following approximate fit to the mean observed radial dependence:Icor/I⊙=1.82 × 10^−6/(r/R⊙)^8 +2.65 × 10^−8/(r/R⊙)^2.22where Icor is the specific intensity at ≈ 500 nm, I⊙ is the disk-center photospheric intensity, andr is the heliocentric radial distance of the observed “impact parameter” (i.e., distance measured inthe plane of the sky)Building an unpolarized beam. In the lectures, it was mentioned that the sum of N ≫ 1plane waves gives an “unpolarized” beam. In this problem you will demonstrate that this is thecase for linear polarization.(a) Construct a collection of N randomly oriented plane waves by successively “adding on” eachwave to a running total for the Stokes parameters. Assume each wave component is in phasewith all others (ensuring linear polarization), and that they all have equal E-field magnitudes.Use whatever random number generation mechanism you like for the transverse orientationangle   of each wave. As each wave is added on (and N is incremented by 1), compute theStokes parameters I, Q, and U for this value of N. Plot the fraction of linear polarizationP =(Q^2 + U^2)^(1/2)/Ias a function of N. Keep going until you get to N = 1000, and use a log-log scale.(b) Repeat the above for at least 100 independent random trials, and compute the mean valueof P for each value of N. Plot that quantity versus N and discuss what you think it means,from a statistics standpoint.

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