158 Week 1 Hwk012717 pdf Question 5: Ray Tracing (II) The sun subtends an angle

Question

158 Week 1 Hwk012717 pdf Question 5: Ray Tracing (II) The sun subtends an angle of about 0.5° in the sky (total that's its angular diameter (not radius) when viewed from earth). a. The distance from the sun to the earth is 150 million km. What is the diameter of the sun? Do not use a calculator (except to check your work, if you want). Instead, use geometry and your Taylor series formulae. Hint: what is 0.5 in radians? (t is good to be able to quickly figure out what 1 is in radians... can you do it? If not, figure it out to l significant digit.) SHOW YOUR WORK. b. The sun shines on a window. which is 1.5m on a side See figure below). Explain clearly what the light profile on the wall looks like dimensions, whether the edges are sharp or fuzzy, and a plot of the liglit intensity vs. distance along the wall for one axis (see second figure you can approximate the sun as square for the purposes of this problem). 5 m

Explanation / Answer

a) Angle subtended (in radians) = Arc / Distance
The diameter of the Sun = distance between Earth and Sun x Angle subtended by the Sun(in rad)

0.5 deg = /360 rad

So, Diameter of Sun = 150000000 x ( / 360)= 13089997 km

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