Moonlit nights and blue skies

I had just joined the PhD program at the Tata Institute of Fundamental Research and was supposed to complete an experimental project. My adviser was Prof. Ojha who taught me photometry, the first thing about astronomy. Photometry involves measuring the amount of light that you receive, say from a star, within a single fairly large range of wavelengths. My project was to measure the eclipses of the binary star Algol.

Tarak, with whom I shared the only telescope we had, was learning spectroscopy. When you measure the amount of light received within many narrow ranges of wavelength, its called spectroscopy. The end product of this process is called a spectrum. We had not yet heard of dreaded Time Allocation Committees and had a jolly good time sharing the telescope. But we soon found out about full Moon nights. These are not good times for astronomers at all. The moonlight would get into the telescope and contaminate the signal from our stars.

We decided to pass the nights by taking measurements of random things, including the moon itself. Its around this time that I had an idea. I thought that if I would make a spectrum of the Moon and one of the Sun, then I would determine how reflective the moon is at different wavelengths. But it turns out that the moons surface is made of grains bigger than the wavelengths I could measure by borrowing the spectrometer Tarak was using. So, the Moons albedo, as it is called, had not much wavelength dependent effect that I could measure. So I had essentially been measuring sunlight in the night.

I still wanted to check. But you cant point your telescope at the Sun. The Sun saturated the spectrometer even if one pointed at it with the naked optical fiber, feeding the instrument. I could not get a spectrum of the sun. The closest I could point the fiber without saturation was still skylight, not sunlight. So, I ended up with a spectrum of the Moon which is the spectrum of the Sun times the Moon’s albedo which is essentially independent of wavelength. I also had a spectrum of skylight which is again the spectrum of the Sun times the Rayleigh scattering cross section of stuff making up our atmosphere.

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Notice how the spectral peak from skylight is noticeably at bluer (shorter) wavelengths than that from moonlight. Both spectra are un-calibrated but they passed through the same instrument. So if you divide one by the other, you are left with the wavelength dependence of the Rayleigh scattering cross section. We had learned in Physics classes that this is a very steep function, inversely proportional to the fourth power of wavelength. The sky supposedly appears blue because Rayleigh scattering is much more effective at bluer (shorter) wavelengths than at redder (longer) ones.

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So, I divided the skylight spectrum by the moonlight spectrum and got a weird curve. One of the important things that I remembered from my Physics classes was to use log-log graphs to make unwieldy power-laws into manageable straight lines. This one turned out to have the correct slope. I was very happy, I had demonstrated to myself that the sky was indeed blue because of Rayleigh scattering. I wrote up a paper for the American Journal of Physics describing how other students can try it out themselves and explore further.

You can find the paper on
arxiv: http://arxiv.org/abs/physics/0702101 or
AJP: http://ajp.aapt.org/resource/1/ajpias/v75/i9/p824_s1

You can read more about Rayleigh scattering on
Wikipedia: http://en.wikipedia.org/wiki/Rayleigh_scattering

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