Background: Design and completely analyze an optical system to measure how fast the Sun is spinning, based on the Doppler shift between the west side of the sun (always turning toward us at velocity v1) and the east side (turning away from us, also at velocity v1). It turns out the Sun has very sharp emission lines at a wavelength of λ = 630.0 nm. You may ignore Earth’s rotation and atmosphere. You’ll need at least 2 parts in your optical system. First, you’ll need to gather (maybe focus, maybe magnify?) the light from only the outer edge of the sun—no more than 5% of its diameter as seen from Earth. Be sure your system blocks out the rest of the sun when taking a measurement of one side or the other. Second, you’ll need to very precisely and accurately separate the sun’s spectrum into different wavelengths so you can measure the difference in wavelength caused by the Doppler shifts. You can use any combination of any optical elements we have discussed in class: lenses, mirrors, pinholes, gratings, single slits, multiple slits. But explain why you chose each item and show mathematically how it fits that role.

Background: Design and completely analyze an optical system to measure how fast the Sun is spinning, based on the Doppler shift between the west side of the sun (always turning toward us at velocity v1) and the east side (turning away from us, also at velocity v1). It turns out the Sun has very sharp emission lines at a wavelength of λ = 630.0 nm. You may ignore Earth’s rotation and atmosphere. You’ll need at least 2 parts in your optical system. First, you’ll need to gather (maybe focus, maybe magnify?) the light from only the outer edge of the sun—no more than 5% of its diameter as seen from Earth. Be sure your system blocks out the rest of the sun when taking a measurement of one side or the other. Second, you’ll need to very precisely and accurately separate the sun’s spectrum into different wavelengths so you can measure the difference in wavelength caused by the Doppler shifts. You can use any combination of any optical elements we have discussed in class: lenses, mirrors, pinholes, gratings, single slits, multiple slits. But explain why you chose each item and show mathematically how it fits that role.